❖ Definition: Flow of charge in a definite direction constitutes electric current
❖ Formulae:
•
\(I=\frac{q}{t}\)
•
\(I=\frac{ne}{t}\)
•
If charge moves in circular orbit: \(I=qf\)
Table 1: Electric Current Basics
Point
Answer
Nature
Scalar quantity
SI unit
Ampere
Unit form
\(C\ s^{-1}\)
1 ampere
\(6.25\times10^{18}\) electrons/second
CGS relation
\(1A=3\times10^9\ statampere\)
Conventional current
Direction of flow of positive charge
Electronic current
Direction of flow of electrons
Conventional vs electronic current
Opposite directions
▢ Electrical Conduction:
Table 1: Charge Carriers in Different Media
Medium
Charge carriers
Metallic conductor
Electrons
Electrolyte
Positive and negative ions
Gases in discharge tubes
Electrons and ions
Semiconductor
Electrons and holes
n-type semiconductor
Mostly electrons
p-type semiconductor
Mostly holes
▢ Drift Velocity:
❖ Definition: Average velocity with which free electrons drift towards positive end of conductor under external electric field
❖ Formula: \(\vec v_d=-\frac{e\vec E}{m}\tau\)
❖ Proportionality: \(v_d\propto E=\frac{V}{l}\)
Table 1: Drift Velocity Points
Point
Answer
\(e\)
Charge of electron
\(m\)
Mass of electron
\(\vec E\)
Applied electric field
\(\tau\)
Relaxation time
Approximate drift velocity
About \(10^{-4}\ m/s\)
Approximate relaxation time
About \(10^{-14}\ s\)
Depends on
Nature of conductor and applied electric field
▢ Relaxation Time:
❖ Symbol: \(\tau\)
❖ Definition: Average time elapsed since each electron suffered its last collision with ion/atom of conductor during drift
❖ Formula: \(\tau=\frac{\lambda}{v_{rms}}\)
Table 1: Relaxation Time
Quantity
Relation
Mean free path
\(\lambda\)
RMS velocity of electrons
\(v_{rms}\)
Temperature relation
\(\tau\propto\frac{1}{Temperature}\)
Temperature increases
Relaxation time decreases
Resistance relation
\(R\propto\frac{1}{\tau}\)
Temperature of conductor increases
Resistance increases and relaxation time decreases
▢ Current and Drift Velocity Relation:
❖ Formula: \(I=venA\)
Table 1: Current-Drift Relation
Symbol
Meaning
\(v\) or \(v_d\)
Drift velocity
\(e\)
Charge of electron
\(n\)
Number of free electrons per unit volume
\(A\)
Area of cross-section
Order of \(n\)
Nearly \(10^{29}/m^3\)
❖ Important Point: Actual signal/energy propagation in conductor occurs through electromagnetic disturbance moving nearly with velocity of light in conductor
▢ Current Density:
❖ Symbol: \(\vec J\)
❖ Definition: Current flowing per unit area normal to current around a point inside conductor
Table 1: Current Density
Quantity
Formula / Point
Current density
\(J=\frac{I}{A}=ven\)
SI unit
\(A\ m^{-2}\)
Nature
Vector quantity
Direction
Direction of flow of positive charge
If area makes angle \(\theta\) with current
\(J=\frac{I}{A\cos\theta}\)
Current through area
\(I=JA\cos\theta=\vec J\cdot\vec A\)
❖ Important Point: Current density is characteristic property of a particular point inside conductor, not whole conductor
▢ Resistance and Conductance:
❖ Resistance Definition: Obstruction offered by conductor to flow of current
❖ Statement: If physical conditions like temperature, nature and dimensions remain constant, current through conductor is directly proportional to potential difference
❖ Formulae:
•
\(I\propto V\)
•
\(I=\frac{V}{R}\)
•
\(V=IR\)
Table 1: Ohm's Law Points
Point
Answer
Valid for
Metallic conductors under constant physical conditions
❖ Important Relation: \(\frac{R_s}{R_p}=n^2\) for \(n\) identical resistors
❖ Voltage Division for Two Series Resistors:
•
\(V_1=\frac{R_1V}{R_1+R_2}\)
•
\(V_2=\frac{R_2V}{R_1+R_2}\)
•
\(V=V_1+V_2\)
❖ Current Division for Two Parallel Resistors:
•
\(I_1=\frac{R_2I}{R_1+R_2}\)
•
\(I_2=\frac{R_1I}{R_1+R_2}\)
•
\(I=I_1+I_2\)
▢ Electric Cell:
❖ Definition: Electric cell is an energy converter, not a source of charge or energy
❖ EMF Definition: Work done per coulomb of charge in moving it through entire closed circuit
Table 1: EMF of Cell
EMF depends on
Details
Plates
Nature of two plates
Electrolyte
Nature, temperature and concentration of electrolyte
Table 2: EMF Independent Of
Independent factor
Point
Quantity of electrolyte
No effect on EMF
Size of electrodes
No effect on EMF
Distance between electrodes
No effect on EMF
❖ Direction of Current:
•
Outside cell: current flows from positive terminal to negative terminal
•
Inside cell: current flows from negative electrode to positive electrode
▢ Internal Resistance:
❖ Symbol: \(r\)
❖ Definition: Resistance of column of liquid between two plates of cell
❖ Depends On:
•
Separation between plates
•
Area of cross-section of liquid column
•
Nature of electrolyte
•
Temperature of electrolyte
•
Degree of dissociation of electrolyte
▢ Terminal Potential Difference:
❖ Definition: Potential difference between two electrodes of a cell in closed circuit
Table 1: Terminal Potential Difference
Condition
Formula / Result
Cell discharging
\(V=E-Ir\), so \(V
Cell charging
\(V=E+Ir\), so \(V>E\)
Open circuit
\(V=E,\ I=0\)
Short circuit
\(R=0,\ V=0\)
General battery terminal p.d.
\(V=E_{eq}-Ir_{eq}\)
❖ Discharging Cell:
•
If current exits from positive terminal, cell is discharging
•
Single cell connected to load is always discharging
•
Terminal p.d.: \(V=E-Ir\)
❖ Charging Cell:
•
If current enters into positive terminal, cell is charging
•
Terminal p.d.: \(V=E+Ir\)
•
During charging, current inside cell is from positive plate to negative plate
•
Direction of voltage is always from negative to positive terminal
▢ Combination of Cells:
Table 1: Series, Parallel and Mixed Grouping of Identical Cells
Quantity
Series
Parallel
Mixed
Arrangement
\(n\) cells in series
\(m\) cells in parallel
\(m\) rows with \(n\) cells each
Total number of cells
\(n\)
\(m\)
\(mn\)
Total emf
\(nE\)
\(E\)
\(nE\)
Total internal resistance
\(nr\)
\(\frac{r}{m}\)
\(\frac{nr}{m}\)
Total resistance with external \(R\)
\(R+nr\)
\(R+\frac{r}{m}\)
\(R+\frac{nr}{m}\)
Current
\(I=\frac{nE}{R+nr}\)
\(I=\frac{E}{R+r/m}=\frac{mE}{mR+r}\)
\(I=\frac{nE}{R+nr/m}=\frac{mnE}{mR+nr}\)
❖ Series Combination Special Cases:
Table 1: Series Cells
Condition
Current / Result
\(R=0\)
\(I=\frac{E}{r}\), same as current due to single cell
\(R\gg nr\)
\(I\approx\frac{nE}{R}\), so \(I\propto n\)
\(R\ll nr\)
\(I\approx\frac{E}{r}\), same as single cell
\(R=r\)
\(I=\frac{nE}{r(1+n)}\)
Terminal p.d. of series battery
\(V=nE-I(nr)=IR\)
Terminal p.d. of individual cell
\(E-Ir\)
❖ Parallel Combination Special Cases:
Table 1: Parallel Cells
Condition
Current / Result
\(R=0\)
\(I=\frac{mE}{r}\)
\(R\gg\frac{r}{m}\)
\(I\approx\frac{E}{R}\), same as single cell
\(R\ll\frac{r}{m}\)
\(I\approx\frac{mE}{r}\), so \(I\propto m\)
\(R=r\)
\(I=\frac{mE}{r(m+1)}\)
Terminal p.d.
\(V=E-I\frac{r}{m}\)
❖ Mixed Combination:
Table 1: Mixed Cells
Condition
Result
Maximum current condition
\(R=\frac{nr}{m}\)
Meaning
External resistance = total internal resistance
Maximum current
\(I_{max}=\frac{mE}{2r}=\frac{nE}{2R}\)
Use
Used when power is required in circuit
❖ Cell Grouping for Maximum Current:
Table 1: Best Grouping
Condition
Best grouping
\(R_{ext}\gg r_{int}\)
Series grouping
\(R_{ext}\ll r_{int}\)
Parallel grouping
\(R_{ext}=r_{int}\)
Mixed grouping
❖ Important Notes:
•
If \(R=r\), same total current flows whether identical cells are connected in series or parallel
•
When cells are connected in series, emf increases
•
When cells are connected in parallel, current capacity increases
❖ Wrongly Connected Cells:
Table 1: Cells Connected Correctly or Wrongly
Condition
Current
\(n\) cells in series, \(m\) cells wrongly connected
\(I=\frac{(n-2m)E}{nr+R}\)
Two different cells correctly connected in series
\(I=\frac{E_1+E_2}{R+r_1+r_2}\)
Two different cells wrongly connected in series
\(I=\frac{E_1-E_2}{R+r_1+r_2}\)
❖ Different Cells in Parallel:
◉ Formula: \(E_{eq}=\frac{\sum E/r}{\sum 1/r}\)
◉ For Two Cells: \(E_{eq}=\frac{E_1/r_1+E_2/r_2}{1/r_1+1/r_2}\)
◉ Note: Use sign according to whether cells are in same or opposite direction
▢ Kirchhoff's Laws:
❖ First Law:
◉ Names: Junction law / current law
◉ Statement: Algebraic sum of currents meeting at a junction is zero
◉ Formula: \(\sum I=0\)
◉ Basis: Conservation of charge
◉ Sign Convention:
•
Current entering junction = positive
•
Current leaving junction = negative
•
Sum of incoming currents = sum of outgoing currents
❖ Second Law:
◉ Names: Loop law / mesh law / voltage law
◉ Statement: In any closed mesh, algebraic sum of potential drops equals algebraic sum of emfs
◉ Formula: \(\sum E=\sum V=\sum IR\)
◉ Basis: Conservation of energy
◉ Sign Convention:
•
While traversing a loop, emf is positive if negative pole of cell is encountered first
•
Emf is negative if positive pole is encountered first
•
\(IR\) is positive if direction of current is same as loop traversal
•
\(IR\) is negative if direction of current is opposite to loop traversal
❖ Potential Difference Example:
◉ Result: \(V_{AB}=V_A-V_B=2V\)
◉ Note: Direction of p.d. is from negative terminal to positive terminal; current flows from positive to negative terminal
▢ Wheatstone Bridge:
❖ Definition: Bridge arrangement of four resistances used for measuring unknown resistance
❖ Balanced Condition: \(\frac{P}{Q}=\frac{R}{S}\)
Table 1: Wheatstone Bridge Points
Condition / Point
Answer
Balanced bridge
Galvanometer shows no deflection
Current through galvanometer
Zero
Potential relation
\(V_B=V_D\)
Most sensitive condition
All four arm resistances nearly equal
\(PS>QR\)
Current flows from D to B
\(PS
Current flows from B to D
Practical applications
Meter bridge, post office box, Carey Foster's bridge
Number of closed circuits
7
Battery and galvanometer interchange
Balance position unaffected
▢ Potentiometer:
❖ Definition: Long uniform wire, generally manganin or constantan, stretched on wooden board
❖ Principle: Potential fall across any length of uniform wire is directly proportional to length if current and area are constant
❖ Formulae:
•
\(V\propto l\)
•
\(V=Kl\)
❖ Potential Gradient: Fall of potential per unit length of wire
Table 1: Potentiometer Formulae
Use
Formula
Comparison of emfs
\(\frac{E_1}{E_2}=\frac{l_1}{l_2}\)
Internal resistance of cell
\(r=\frac{l_1-l_2}{l_2}R\)
Internal resistance using emf and terminal p.d.
\(r=\left(\frac{E}{V}-1\right)R\)
Table 2: Potentiometer Properties
Point
Answer
Ideal instrument
Ideal voltmeter
Accuracy
Most accurate for measuring emf/potential difference
Method
Null deflection method
Measures potential
Point to point
Used to
Calibrate voltmeter
Sensitivity increased by
Decreasing potential gradient
Sensitivity increased by
Increasing length of potentiometer wire
For fixed wire length
Reduce current using rheostat
❖ Symbols:
•
\(l_1,l_2\) = balancing lengths
•
\(K\) = potential gradient
•
\(R\) = external resistance connected in internal resistance experiment
▢ Meter Bridge:
❖ Also Called: Slide wire bridge
❖ Principle: Based on Wheatstone bridge principle
❖ Construction: 1 m long wire soldered to ends of two rectangular metallic strips
Table 1: Meter Bridge Formulae
Quantity
Formula
Balance condition
\(\frac{R_1}{R_2}=\frac{l}{100-l}\)
Unknown resistance
\(R_2=\frac{100-l}{l}R_1\)
Table 2: Meter Bridge Points
Point
Answer
\(R_1\)
Known resistance
\(R_2\)
Unknown resistance
\(l\)
Balancing length in cm
Very high/low resistances
Cannot be measured accurately
Battery and galvanometer interchange
Balance point unaffected
▢ Special Resistance Networks:
Table 1: Equivalent Resistance Results
Network / Condition
Equivalent / Result
Arms AB and BC: 30Ω + 30Ω = 60Ω in parallel with AC = 30Ω
\(R_p=\frac{30\times60}{30+60}=20\Omega\)
For \(V=2V\) in above network
\(I=\frac{2}{20}=0.1A\)
Three equal resistors in parallel along AB
\(R_{AB}=\frac{R}{3}\)
Balanced Wheatstone type with equal resistances
No current in bridge resistor
Equivalent between X and Y in balanced network
\(R_{eq}=R\)
▢ Read and Digest:
Table 1: Important Points
Fact
Answer
Electric current
Scalar; has direction but does not obey parallelogram law
Electric current
Due to flow of positive and negative charges
Metallic conductor current
Due to electrons only
Gas discharge tube current
Due to electrons and positive ions
Constantan wire
Used for standard resistance due to negligible temperature coefficient
Resistivity
Depends only on material and temperature
Resistivity independent of
Length, cross-section and mass of wire
Resistance depends on
Size, geometry, temperature and internal structure
Resistance of metals with temperature
Increases
Resistance of semiconductors/electrolytes with temperature
Decreases
Impurities in conductor
Increase resistance
Impurities in semiconductor
Decrease resistance
Resistance with density decrease
Increases
Mean velocity of electrons due to random motion
Zero
Mean speed and temperature
\(v\propto\sqrt T\)
Ohm's law
\(v_d\propto E\)
Thermistor
Large negative temperature coefficient
Thermistor use
Resistance thermometers / measuring low temperature changes
Thermistors prepared from
Metal oxides: oxide-coated nickel, oxides of strontium and barium
Electrolytes obey Ohm's law
At high potential
Steady current in uniform conductor segment
Net charge in any segment is zero
Semiconductor at 0 K
Behaves as insulator
Terminal p.d. in short circuit
Zero
Cells in series
EMF increases
Cells in parallel
Current capacity increases
Potentiometer
Best instrument to measure emf accurately
Potentiometer accuracy reason
Measures potential in open circuit
Wheatstone bridge closed circuits
7
Wheatstone bridge balance point
Unaffected by interchanging battery and galvanometer
▢ High-Yield Recall:
Table 1: Electric Current One-Liners
Fact
Answer
Electric current
\(I=\frac{q}{t}\)
Charge in circular orbit
\(I=qf\)
1 ampere
\(6.25\times10^{18}\) electrons/s
Current nature
Scalar
Conventional current
Direction of positive charge flow
Electronic current
Opposite to conventional current
Metal conduction
Electrons
Electrolytic conduction
Positive and negative ions
Drift velocity
\(\vec v_d=-\frac{e\vec E}{m}\tau\)
Drift velocity relation
\(v_d\propto E\)
Relaxation time
\(\tau=\frac{\lambda}{v_{rms}}\)
Temperature and relaxation time
\(\tau\propto\frac{1}{T}\)
Resistance and relaxation time
\(R\propto\frac{1}{\tau}\)
Current and drift velocity
\(I=venA\)
Current density
\(J=\frac{I}{A}=ven\)
Current through angled area
\(I=\vec J\cdot\vec A\)
Resistance
\(R=\rho\frac{l}{A}\)
Resistivity
\(\rho=\frac{m}{ne^2\tau}\)
Conductance
\(G=\frac{1}{R}\)
Conductivity
\(\sigma=\frac{1}{\rho}\)
Ohm's law
\(V=IR\)
I-V slope
\(\frac{I}{V}=\frac{1}{R}\)
Metal resistance with temperature
Increases
Semiconductor resistance with temperature
Decreases
Resistance-temperature formula
\(R_t=R_0(1+\alpha t)\)
Temperature coefficient
\(\alpha=\frac{R_t-R_0}{R_0t}\)
Manganin/constantan
Very small \(\alpha\)
Superconductor
\(R=0\)
Stretching wire
\(R\propto l^2\)
Area change
\(R\propto\frac{1}{A^2}\)
Radius change
\(R\propto\frac{1}{r^4}\)
Series resistance
\(R=R_1+R_2+...\)
Parallel resistance
\(\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+...\)
n identical series resistors
\(nR\)
n identical parallel resistors
\(\frac{R}{n}\)
Voltage division
\(V_1:V_2=R_1:R_2\)
Current division
\(I_1:I_2=\frac{1}{R_1}:\frac{1}{R_2}\)
Cell
Energy converter
Discharging cell p.d.
\(V=E-Ir\)
Charging cell p.d.
\(V=E+Ir\)
Open circuit
\(V=E, I=0\)
Short circuit
\(V=0\)
Series cells current
\(I=\frac{nE}{R+nr}\)
Parallel cells current
\(I=\frac{mE}{mR+r}\)
Mixed cells current
\(I=\frac{mnE}{mR+nr}\)
Mixed grouping maximum current
\(R=\frac{nr}{m}\)
Kirchhoff junction law
\(\sum I=0\)
Kirchhoff loop law
\(\sum E=\sum IR\)
Wheatstone bridge
\(\frac{P}{Q}=\frac{R}{S}\)
Meter bridge
\(\frac{R_1}{R_2}=\frac{l}{100-l}\)
Potentiometer principle
\(V\propto l\)
Comparison of emf
\(\frac{E_1}{E_2}=\frac{l_1}{l_2}\)
Internal resistance by potentiometer
\(r=\frac{l_1-l_2}{l_2}R\)
Potentiometer
Ideal voltmeter / null deflection method
Q1.
Resistance of wire is R. If length is halved and diameter doubled, new resistance is
📅CEE MBBS 2025
Q2.
A house is connected to 220 V supply protected by 9 A fuse. Maximum number of 60 W bulbs in parallel is
📅CEE MBBS 2025
Q3.
The slope of graphical representation of Ohm's law i.e. voltage versus current is:
📅CEE Nursing 2024
Q4.
Radius of conductor is increased by 2 times, the specific resistance will be:
📅CEE Nursing 2024
Q5.
A uniform wire of resistance 36 Ω is bent in the form of a circle. A battery is connected between positions A and B such that the smaller arc subtends \(60^\circ\) at the centre. The effective resistance between A and B is:
📅CEE MBBS 2024B
Q6.
When a potential difference V is applied across a conductor at temperature T, the drift velocity of electrons is proportional to:
📅CEE MBBS 2024B
Q7.
The resistance of a material at 20°C is 1.72 Ω. Then its resistance at 100°C is: [α = 0.0039 K⁻¹]
📅CEE MBBS 2024a
Q8.
A length of a wire is stretched by 0.1%. The resistance change will be:
📅CEE MBBS 2024a
Q9.
If the radius of a conductor is increased by 2 times, then its specific resistance will be:
📅CEE MBBS 2024a
Q10.
A wire 50 cm long and 1 mm² in cross-section carries a current of 4 A when connected to a 2 V battery. The resistivity of the wire is:
📅CEE MBBS 2023
Q11.
Find the equivalent resistance between A and B in the resistor network shown in the source figure, where each resistor is \(1\,\Omega\).
📅CEE MBBS 2023
Q12.
When current \(I\) is flowing through a conductor, drift velocity is \(v\). If both current and cross-sectional area are doubled, the new drift velocity is:
📅CEE MBBS 2023
Q13.
The slope of the graph of Ohm's law, voltage versus current, is:
📅CEE MBBS 2022
Q14.
If a copper wire is stretched so its length increases by 0.1%, the percentage increase in its resistance is approximately:
📅CEE MBBS 2022
Q15.
What happens to the product of resistivity and conductivity if temperature of a conductor is increased?
📅CEE MBBS 2022
Q16.
Drift velocity is independent of:
📅CEE MBBS 2022
Q17.
If a wire is stretched to double its length while volume remains constant, its resistance becomes:
📅CEE MBBS 2021
Q18.
Two wires of resistivities \( \rho_1\) and \( \rho_2\), having equal length and cross-sectional area, are joined in series. The equivalentnt resistivity is:
📅CEE MBBS 2021
Q19.
Which formula is used to calculate the value of electrical conductivity (σ) of a material where 'J' is current density and 'E' is the electric field:
📅CEE BDS 2024
Q20.
In the absence of an electric field, the mean velocity of free electrons in a conductor at absolute temperature (T) is:
📅CEE BDS 2024
Q21.
Find the value of current I in the given circuit diagram.
📅CEE BDS 2023
Q22.
The resistance of wire depends upon which of the following factors?
📅CEE BDS 2023
Q23.
If the length of wire is stretched to double, resistance becomes:
📅CEE BDS 2021
Q24.
Number of electrons per second travelled if we apply 1 μ ampere current is:
📅CEE BDS 2021
Q25.
A wire of resistance 2Ω is stretched 2 times, the resistance will be:
📅CEE BDS 2021
Q26.
An electric cable of copper has just one wire of radius 9 mm. It's resistance is 5Ω. This single copper wire of cable is replaced by six different well insulated copper wires each of radius 3 mm. The total resistance of the cable now be equal to
📅BP 2014
Q27.
The ratio of current and charge carriers in two conductors of same cross sectional area are \(\frac{7}{4}\) and \(\frac{5}{4}\) respectively then the ratio of drift velocity in two conductors will be:
📅BP 2014
Q28.
6 cells of emf 6V are connected in parallel combination. What is the equivalent emf?
📅BP 2012
Q29.
Find the value of current flow in circuit where the cell has negligible internal resistance.
📅BP 2012
Q30.
The resistance of wire of length 'L' and diameter d is R. The wire is stretched to reduce its diameter to 1/3. The ratio of final resistance to original resistance will be:
📅BP 2012
Q31.
The resistance 'R' from following graph is:
📅BP 2010
Q32.
If a wire of resistance R is stretched n times then resistance becomes:
📅MOE 2014•BP 2017
Q33.
A coil when connected with 200 V main dissipates 400 watts. The resistance of the coil is ... ohm.
📅IOM
Q34.
Series combination of 2Ω and 3Ω resistors are connected in parallel to the series combination of 1Ω and 4Ω resistors. The whole combination is further connected to a battery of 10V and internal resistance 1Ω. The potential difference between the ends of 4Ω resistor will be:
📅MOE 2013
Q35.
The resistance of a conductor is 15Ω at 60°C and 20Ω at 100°C. The resistance at 40°C is
📅MOE 2012
Q36.
A wire of length 10 cm is stretched to 20 cm. The resistance of the stretched wire changes to:
Q37.
The resistance of a conductor is 10Ω at 60°C and 15Ω at 100°C. The resistance at 0°C is:
📅MOE 2011
Q38.
The terminal potential difference of a circuit having a cell of emf 6V with internal resistance 2Ω and external resistance 8Ω is:
📅MOE 2011
Q39.
A wire of resistance 2Ω is stretched 1.5 times, the resistance of stretched wire becomes:
📅MOE 2011
Q40.
The terminal potential difference of a circuit having 9V cell, 2Ω internal resistance and 10Ω external resistance is:
📅MOE 2011
Q41.
A wire of resistance 2Ω is stretched 2 times, the resistance will be:
📅MOE 2011
Q42.
The resistance of 20 cm length of wire is 5 ohms. When the wire is stretched to 40 cm, the new resistance becomes:
📅IOM 2014
Q43.
In DC circuit, power dissipated per unit volume is proportional to:
📅IOM 2013
Q44.
When a battery of voltage 'E' with internal resistance 'r' is connected to a circuit of resistance 'R', the terminal voltage is:
📅IOM
Q45.
One of the following is an ohmic conductor:
📅IOM
Q46.
'n' identical cells in series grouping all in same order have a total emf of 15V when one cell is reversed gives 12V. The number 'n' will be:
📅IOM 2011
Q47.
What is the potential drop across an electric hot plate which draws 5A when its resistance is 24Ω?
📅IOM 2010
Q48.
5 resistors each of resistance r are so connected that 3 of them are in parallel while the remaining 2 are in series with this parallel combination. The net resistance is:
📅KU 2014/BP 2016,2017
Q49.
A metal wire of length L and uniform cross-sectional area A has resistance of 100Ω. It is stretched with 5% length increase. The volume of the wire remains constant. What is the new resistance of stretched wire?
Q50.
Which statement about dry cell is NOT correct?
📅KU 2014
Q51.
Resistances of 6Ω each are connected as shown with current 0.5A. The potential difference VP-VQ is:
📅KU 2014
Q52.
In the circuit, find V1
📅KU 2010
Q53.
Three resistances of 4Ω each are connected as shown. If point D divides the resistance into two equal halves, the resistance between A and D is:
📅IE 2010
Q54.
Find the equivalent resistance between points A and B in the given figure:
📅IE 2011
Q55.
In metals, conduction of electricity is due to:
Q56.
Find out the equivalent resistance of the given circuit (R₁ = 100Ω, R₂ = 50Ω, R₃ = 50Ω, R4)=75Ω
📅IE 2013
Q57.
For two conductors, if the ratio of electron density is 5/3 and current density is 3/5, the ratio of drift velocities is:
📅BP 2014
Q58.
There are 8 equal resistors, each of resistance R, in a circuit. Four groups, each consisting of two resistors connected in series, are connected in parallel. The total resistance of the system will be:
📅MOE 2014
Q59.
One type of charger for a mobile phone supplies a current of 240 mA for one hour. How many electrons flow to the mobile phone?
📅KU 2011
Q60.
Net charge in a current-carrying conductor is:
📅KU 2013
Q61.
As temperature of a metallic resistor increases, the product of resistivity and conductivity:
📅KU 2012
Q62.
If the power of a heater is 1 W and a current of 1 A passes through it, find its resistance.
📅KU 2010
Q63.
A wire has a resistance of 1.7 Ω at 20°C. If the temperature coefficient of resistance of the wire is 0.0093/°C, then its resistance at 100°C will be:
📅Bangladesh 09
Q64.
A cell of e.m.f. X is connected across a resistance R. The potential difference across the resistance is measured as Y. Then the internal resistance of the cell should be:
📅Bangladesh 09
Q65.
The unit of electrical conductivity is:
📅KU 09
Q66.
5 cells each of emf E and internal resistance r are connected in series. By mistake one of the cells was connected wrongly. The equivalent emf and internal resistance will be:
📅IOM 2066
Q67.
If radius of a conducting wire is doubled, its specific resistance:
📅KU 08
Q68.
The circuit shows a bulb and a battery connected together by a conducting wire. Which of the following is true for the current in the above circuit?
📅KU 08
Q69.
A bulb and a battery were initially connected in the circuit. Now an uncharged capacitor is connected in the same circuit. Then:
📅KU 08
Q70.
Wheatstone bridge measures:
Q71.
Resistors of resistance 1 Ω each are connected as shown in the figure with a 15 V battery. Current in the circuit is:
📅MOE 2056
Q72.
The quantity analogous to temperature in electricity is:
📅MOE 2055
Q73.
Diameter of a Nichrome wire is halved. New resistance is:
📅MOE 2055
Q74.
Two 1Ω resistors are connected in parallel. The combination is again connected in series with a 2 Ω resistor. The whole arrangement is then joined to a 10 V battery. The current through any one of the 1 Ω resistors is:
📅MOE 2054
Q75.
An electric cell has e.m.f. 2 V and internal resistance 0.1Ω; the external resistance in the circuit is 3.9 Ω. What is the value of the potential difference between the two ends of the shunt?
📅MOE 2053
Q76.
The emf of a source doing 5J work by 10C charge is:
📅MOE
Q77.
Flow of 6.25 × 1018 electrons/s contributes to current:
📅MOE 2058
Q78.
Three resistors R₁, R₂ and R₃ ohms are connected in a parallel combination. If R₁ < R₂ < R₃, the equivalent resistance will be:
📅MOE 2058
Q79.
If a copper wire is stretched to make it 0.1% longer, the percentage change in its resistance will be:
📅MOE 2000
Q80.
A wire of resistance 16Ω is bent into circular form. Then the equivalent resistance between two points of any diameter is:
📅MOE 2008
Q81.
If two resistances of values 4.5Ω and 5.5Ω respectively are connected in series and a third resistance of 10Ω is connected in parallel with both of these, the total resistance of the system will be:
📅MOE 2064
Q82.
The diameter of a Nichrome wire is reduced to half. Now the resistance changes by:
📅MOE 2064
Q83.
A battery of emf 12V is connected in parallel with a voltmeter. The voltmeter reads 11V. This is because of the:
📅MOE 2064
Q84.
The relation between drift velocity and electric field to obey Ohm's law accurately is:
📅MOE 2063
Q85.
Three equal resistors, each of resistance R, are connected so as to form an equilateral triangle. The equivalent resistance at any two corners is:
📅MOE 2066
Q86.
The resistance of two wires connected in parallel is 3.43Ω while the resistance of the same wires connected in series is 14Ω. The resistances are:
📅IOM 2008
Q87.
The specific resistance of a wire 1.1m long and 0.4mm in diameter having a resistance of 0.42Ω will be:
📅IOM 2008
Q88.
A piece of wire of resistance 4Ω is bent through 180° at its midpoint and the two halves are twisted together. Their resistance is:
📅IOM 2004
Q89.
When 5.5Ω and 4.5Ω resistances are joined together in series and a 10Ω resistance is joined in parallel, the final resistance of the system is:
📅IOM 2003
Q90.
Which of the following relations is called current density?
📅IE 2004
Q91.
A potentiometer consists of wire of length 4m and resistance 10Ω. It is connected to a cell of emf 2V. The potential difference per unit length of the wire will be:
📅IE 2004
Q92.
The potential difference across a resistance is 12V and the internal resistance of the cell is 0.02Ω. If the cell is delivering a current of 10.4A, then the emf of the cell is:
📅IE 2005
Q93.
The equivalent resistance of a network of three 4Ω resistors cannot be:
📅IE 2007
Q94.
A meter of internal resistance R can measure a maximum voltage of 10mV. For it to measure a maximum voltage of 10V, we have to:
📅IE 2001
Q95.
Two resistors are joined in parallel whose resultant is 6/5Ω. One of the resistance wires is broken and the effective resistance is 2Ω. The resistance of the wire that got broken was:
📅MOE 2010
Q96.
What is the current supplied by the battery in the circuit shown in the figure?
📅BPKIHS 1995
Q97.
A battery of emf E and internal resistance r is used in a circuit with a variable external resistance R. Then the value of R for which the power consumed in R is maximum is:
📅BPKIHS 1997
Q98.
Potentiometer is a device based on the principle that potential difference across the potentiometer wire is:
📅BPKIHS 2005
Q99.
There are two wires A and B. The radius of B is one fourth of A. Then the ratio of resistance of B to A, if both are of the same material, is:
📅BPKIHS 2006
Q100.
Which of the following quantities does not change when a resistor connected to a battery is heated due to current?
📅BPKIHS 1997
Q101.
If the radius of a copper wire carrying a current is doubled, the drift velocity of electrons will:
📅MOE 2010
Q102.
A cell of emf 1.5V having a certain internal resistance is connected to a load of 2Ω. For maximum power transfer, the internal resistance of the cell in ohms should be:
Q103.
If a copper wire is stretched to make it 0.1% thinner, then the percentage increase in resistance would be nearly:
Q104.
In a Wheatstone's bridge, the battery and galvanometer are interchanged. The condition for balance:
Q105.
When a potential difference is applied across a conductor, only the electrons drift and the current flowing is I. If the positive ions had also drifted, then the current would have been:
Q106.
Out of 3 equal resistances, how many different combinations are possible?
Q107.
An external resistance R is connected to a cell of emf E and internal resistance r. The current in the external circuit is maximum when:
Q108.
A 1000 watt heating unit is designed to operate on a 120V line. The line voltage drops to 110V. The percentage of heat output drops by:
Q109.
A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled if:
Q110.
Three resistances 2Ω, 3Ω and 5Ω are connected in parallel and a potential difference of 20V is applied across the terminals of the combination. The potential difference across the 3Ω resistance is:
Q111.
A uniform wire of resistance RΩ is divided into ten equal parts and all of them are connected in parallel. The equivalent resistance will be:
Q112.
Masses of three wires of the same material are in the ratio 1:2:3 and their lengths are in the ratio 3:2:1. Electrical resistance of these wires will be in the ratio:
Q113.
The resistance of a conductor is 5Ω at 50°C and 6Ω at 100°C. What is the resistance at 0°C?
Q114.
The length of a conductor is halved. Its conductivity will be:
Q115.
A square aluminium rod is 1m long and 5mm on edge. What must be the radius of another aluminium rod whose length is 1m and which has the same resistance as the previous rod?
Q116.
Two wires of the same dimensions but resistivities ρ₁ and ρ₂ are connected in series. The equivalent resistivity of the combination is:
Q117.
A 1kg piece of copper is drawn into a wire 1mm thick and another piece into a wire 2mm thick. Compare the resistance of these wires:
Q118.
Two unequal resistances are connected in series with a cell. Which of the following statements is true?
Q119.
Four wires of the same length, diameter and material are connected to each other to form a square. If the resistance of each wire is R, then equivalent resistance across the opposite corners is:
Q120.
A primary cell of emf 2V, when short-circuited gives a current of 4A. Its internal resistance in ohm will be:
Q121.
As shown in the figure, the current flowing in the 2RΩ resistor is:
Q122.
A battery is connected to an external circuit. The potential drop within the battery is proportional to:
Q123.
The emf of a generator is 6V and internal resistance is 0.5kΩ. The reading of a voltmeter having an internal resistance of 2.5kΩ is:
Q124.
A copper wire of resistance R is cut into ten parts of equal length. Two pieces are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance:
Q125.
When a current of 2A flows in a battery from negative to positive terminal, the p.d. across it is 12V. If a current of 3A flowing in the opposite direction produces a p.d. of 15V, the emf of the battery is:
Q126.
A cell supplies a current I₁ through a resistance R₁ and a current I₂ through a resistance R₂. The internal resistance of the cell is:
Q127.
Five cells each of internal resistance 0.2Ω and emf 2V are connected in series with a resistance of 4Ω. The current through the external resistance is:
Q128.
A battery is made by connecting 6 cells each having capacity 5Ah at 1.5V. The battery will have capacity equal to:
Q129.
Two identical cells send the same current in a 3Ω resistance, whether connected in series or in parallel. The internal resistance of each cell should be:
Q130.
Three similar cells, each of emf 2V and internal resistance r, send the same current through an external resistance of 2Ω when connected in series or in parallel. The strength of current flowing through the external resistance is:
Q131.
A battery of internal resistance r having no lead resistance has an emf E volt. What is the observed emf across the terminals of the battery when a load resistance R (= r) is connected to its terminals?
Q132.
A, B, C and D are four resistances of 2Ω, 2Ω, 2Ω and 3Ω respectively. They are used to form a Wheatstone bridge. The resistance D is short-circuited with a resistance R in order to get the bridge balanced. The value of R will be:
Q133.
Two cells having emf and internal resistance 10V, 5Ω and 6V, 3Ω are connected in series with unlike plates joined together through a load of 2Ω. Then the p.d. of each cell is:
Q134.
Two cells of 10V, 5Ω and 6V, 3Ω are joined in series with like plates joined together through a load of 2Ω. Then p.d. of each cell is:
Q135.
Two cells of equal emf E and different internal resistances r₁ and r₂ are connected in series through a variable load of R. Then the value of R so that p.d. across the first cell is zero is:
Q136.
n identical cells, each of emf E and internal resistance r, are joined in series with two cells A and B connected wrongly. Find the p.d. across A or B (n > 4):
Q137.
24 cells each of 2V and 1Ω are joined in mixed combination through 6Ω. Pmax and Imax will be:
Q138.
A battery is delivering a maximum power of 24W in a load. The circuit is under maximum power condition and supplying a maximum current of 2A. Emf and internal resistance of the battery will be:
Q139.
To get a maximum current through a resistance of 2.5Ω, one can use m rows of cells, each row having n cells. The internal resistance of each cell is 0.5Ω. What are the values of m and n if the total number of cells is 20?
Q140.
Two identical cells connected in series send 1A current through a 5Ω resistor. When they are connected in parallel they send 0.8A current through the same resistor. What is the internal resistance of the cell?
Q141.
Two square metal plates of same thickness and material are connected in series. The side of B is twice that of A. Then the ratio of their resistance is:
Q142.
Figure represents a part of closed circuit. The p.d. between points A and B (Vₐ - Vᵦ) is:
Q143.
A battery of emf 10V is connected to resistances as shown in the figure. What is the potential difference between A and B?
Q144.
For what value of unknown resistance x will the potential difference between B and D be zero in the arrangement shown?
Q145.
A uniform wire of resistance 36Ω is bent in the form of a circle. Then effective resistance across the points A and B, which subtend an angle of 30° at the centre, is:
Q146.
A current of 1mA flows through a copper wire. How many electrons will pass a point in each second?
Q147.
A current through a wire depends on its time as I = 10 + 4t. The charge crossing through the section of the wire in 10 seconds is:
Q148.
A wire has non-uniform cross-section. It carries a current I. The drift velocity of electrons as the cross-sectional area increases from A to B:
Q149.
A potential difference V is applied across a conductor having length l and thickness t. If thickness is doubled then vd will become/remain:
Q150.
What is the total momentum of electrons in the wire having 100m length and carrying 10A current?
Q151.
A 10m long wire of resistance 20Ω is connected in series with a battery of emf 6V and a resistance of 10Ω. The potential gradient along the wire in volt per meter is:
Q152.
A cell can be balanced against 110cm and 100cm of potentiometer wire respectively when in open circuit and when short-circuited through a resistance of 10Ω. Find the internal resistance of the cell:
Q153.
The length of a potentiometer wire is 5 meters. An electron in this wire experiences a force of 4.8 × 10⁻¹⁹ N. The emf of the cell used in potentiometer is:
Q154.
If the resistance of ammeter (Rₐ) is connected across the series and voltmeter of resistance (Rᵥ) across the parallel, then to measure the value of R:
📅KU 2016
Q155.
The radius of a conductor is doubled, resistance will be:
📅KU 2017
Q156.
The wire has resistance 32Ω. When its length is doubled, then percentage increase in resistance will be:
📅IOM 2017
Q157.
The resistance of a wire is 4Ω. When it is bent through 180° and twisted together, then the new resistance will be:
