Electric current | CEE Academy

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ELECTRIC CURRENT

▢ Current:

❖ Definition: Flow of charge in a definite direction constitutes electric current

❖ Formulae:

•
\(I=\frac{q}{t}\)
•
\(I=\frac{ne}{t}\)
•

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:

▢ 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:

▢ 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
	\(J=\frac{I}{A\cos\theta}\)
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

❖ Formula: \(R=\rho\frac{l}{A}\)

❖ Resistivity Formula: \(\rho=\frac{m}{ne^2\tau}\)

Table 1: Resistance and Resistivity

Quantity	Depends on	Independent of
Resistance \(R\)	Temperature, nature, dimensions of conductor	—
Resistivity \(\rho\)	Temperature and nature of material	Length, area, dimensions

Table 2: Units

Quantity	Formula	Unit
Resistance	\(R\)	Ohm \((\Omega)\)
Resistivity	\(\rho\)	Ohm-metre \((\Omega m)\)
Conductance	\(G=\frac{1}{R}\)	\(\Omega^{-1}\), siemen, mho
Conductivity	\(\sigma=\frac{1}{\rho}=\frac{l}{RA}\)

▢ Ohm's Law:

❖ 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
Ohmic conductors	Obey Ohm's law
V-I graph for ohmic conductor	Straight line through origin
Non-ohmic conductors	Do not obey Ohm's law
V-I graph for non-ohmic conductor	Not a straight line
Examples of non-ohmic conductors	Diode valve, neon gas, junction diode, electrolytes, carbon compounds

❖ Graph:

◉ Slope of I-V Graph: \(m=\tan\theta=\frac{I}{V}=\frac{1}{R}\)

◉ More Slope: Less resistance

◉ Different Temperature: Different V-I graphs

❖ Resistance Increases With:

•
Decrease in density
•
Mechanical stress
•
Impurities in conductor

▢ Variation of Resistance with Temperature:

❖ Formula: \(R_t=R_0(1+\alpha t)\)

❖ Temperature Coefficient: \(\alpha=\frac{R_t-R_0}{R_0t}\)

❖ **table:

◈ caption: Material-wise Temperature Coefficient

◈ data:

Material
\(\alpha\)
Resistance with temperature

Metals
Positive
Increases

Semiconductors
Negative
Decreases

Insulators
Negative
Decreases

Alloys like manganin, eureka, constantan
Very small
Used for standard resistances

Superconductors
Zero
Resistance zero

❖ Two Temperature Formula: \(\alpha=\frac{R_2-R_1}{R_1t_2-R_2t_1}\)

▢ Recasting of Resistance:

❖ Constant Volume: \(A_1l_1=A_2l_2=constant\)

❖ **table:

▢ Combination of Resistances:

❖ **table:

❖ 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:

❖ 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	\(I=\frac{nE}{R+nr}\)	\(I=\frac{E}{R+r/m}=\frac{mE}{mR+r}\)

❖ Series Combination Special Cases:

◉ _*table:

❖ Parallel Combination Special Cases:

◉ **table:

❖ Mixed Combination:

◉ **table:

❖ Cell Grouping for Maximum Current:

◉ **table:

❖ Important Notes:

•
•
When cells are connected in series, emf increases
•
When cells are connected in parallel, current capacity increases

❖ Wrongly Connected Cells:

◉ **table:

❖ 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:

■ _*type: bullet

While traversing a loop, emf is positive if negative pole of cell is encountered first
Emf is negative if positive pole is encountered first

❖ 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
•

▢ 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:

▢ 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:

Q1.

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

Q2.

The ratio of current and charge carriers in two conductors of same cross sectional area and n₁/n₂ = 1/2 respectively then the ratio of drift velocity in two conductors will be:

📅BP 2014

Q3.

6 cells of emf 6V are connected in parallel combination. What is the equivalent emf?

📅BP 2012

Q4.

Find the value of current flow in circuit where the cell has negligible internal resistance.

📅BP 2012

Q5.

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

Q6.

The resistance 'R' from following graph is:

📅BP 2010

Q7.

If a wire of resistance R is stretched n times then resistance becomes:

📅MOE 2014•BP 2017

Q8.

A coil when connected with 200 V main dissipates 400 watts. The resistance of the coil is ... ohm.

📅IOM

Q9.

Series combination of 2Ω and 3Ω resistors are connected in parallel to the series combination of 1Ω and 2Ω 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

Q10.

The resistance of a conductor is 15Ω at 60°C and 20Ω at 100°C. The resistance at 40°C is

📅MOE 2012

Q11.

A wire of length 10 cm is stretched to 20 cm. The resistance of the stretched wire changes to:

Q12.

The resistance of a conductor is 10Ω at 60°C and 15Ω at 100°C. The resistance at 0°C is:

📅MOE 2011

Q13.

The terminal potential difference of a circuit having a cell of emf 6V with internal resistance 2Ω and external resistance 8Ω is:

📅MOE 2011

Q14.

A wire of resistance 2Ω is stretched 1.5 times, the resistance of stretched wire becomes:

📅MOE 2011

Q15.

The terminal potential difference of a circuit having 9V cell, 2Ω internal resistance and 10Ω external resistance is:

📅MOE 2011

Q16.

A wire of resistance 2Ω is stretched 2 times, the resistance will be:

📅MOE 2011

Q17.

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

Q18.

In DC circuit, power dissipated per unit volume is proportional to:

📅IOM 2013

Q19.

When a battery of voltage 'E' with internal resistance 'r' is connected to a circuit of resistance 'R', the terminal voltage is:

📅IOM

Q20.

One of the following is an ohmic conductor:

📅IOM

Q21.

'n' identical cells in series (total emf 15V) when one cell is reversed gives 12V. The number 'n' is:

📅IOM 2011

Q22.

What is the potential drop across an electric hot plate which draws 5A when its resistance is 24Ω?

📅IOM 2010

Q23.

5 resistors (each resistance r) are connected with 3 in parallel and 2 in series with this combination. The net resistance is:

📅KU 2014/BP 2016,2017

Q24.

A metal wire (L, A, R=100Ω) is stretched with 5% length increase (volume constant). New resistance is:

Q25.

Which statement about dry cell is NOT correct?

📅KU 2014

Q26.

Resistances of 6Ω each are connected as shown with current 0.5A. The potential difference V_P-V_Q is:

📅KU 2014

Q27.

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:

Q28.

Find the equivalent resistance between points A and B in the given figure:

📅IE 2011

Q29.

In metals, conduction of electricity is due to:

Q30.

Find out the equivalent resistance of the given circuit (R₁ = 100Ω, R₂ = 50Ω, R₃ = 50Ω):

📅IE 2013

Q31.

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

Q32.

Eight equal resistors (R) are connected with four groups of two resistors in series, all in parallel. Total resistance is:

📅MOE 2014

Q33.

A mobile phone charger supplies 240 mA for 1 hour. Number of electrons flowing is:

📅KU 2011

Q34.

Net charge in a current-carrying conductor is:

📅KU 2013

Q35.

As temperature of a metallic resistor increases, the product of resistivity and conductivity:

📅KU 2012

Q36.

A heater has power 1W with 1A current. Its resistance is:

📅KU 2010

Q37.

A wire (R = 1.7Ω at 20°C, α = 0.0093/°C) has resistance at 100°C:

📅Bangladesh 09

Q38.

A cell (emf X) connected across resistance R shows potential difference Y. Internal resistance is:

📅Bangladesh 09

Q39.

The unit of electrical conductivity is:

📅KU 09

Q40.

Five cells (each E, r) in series with one wrongly connected have equivalent emf and internal resistance:

📅IOM 2066

Q41.

If radius of a conducting wire is doubled, its specific resistance:

📅KU 08

Q42.

In a circuit with a bulb and battery, current is:

📅KU 08

Q43.

When an uncharged capacitor is added to a bulb-battery circuit:

📅KU 08

Q44.

Wheatstone bridge measures:

Q45.

Resistors (1Ω each) are connected as shown with 15V battery. Current in the circuit is:

📅MOE 2056

Q46.

The quantity analogous to temperature in electricity is:

📅MOE 2055

Q47.

Diameter of a Nichrome wire is halved. New resistance is:

📅MOE 2055

Q48.

Two 1Ω resistors in parallel, in series with 20Ω, connected to 10V battery. Current through any 1Ω resistor is:

📅MOE 2054

Q49.

A cell (2V, 0.1Ω) with external resistance 3.9Ω has potential difference:

📅MOE 2053

Q50.

The emf of a source doing 5J work by 10C charge is:

📅MOE

Q51.

Flow of 6.25 × 10¹⁸ electrons/s contributes to current:

📅MOE 2058

Q52.

Three resistors (R₁, R₂, R₃ with R₁ < R₂ < R₃) in parallel have equivalent resistance:

📅MOE 2058

Q53.

If a copper wire is stretched 0.1% longer, percentage change in resistance is:

📅MOE 2000

Q54.

A wire (16Ω) bent into a circle has equivalent resistance between diameter points:

📅MOE 2008

Q55.

Resistors 4.5Ω and 5.5Ω in series with 10Ω in parallel give total resistance:

📅MOE 2064

Q56.

Diameter of Nichrome wire halved. Resistance change factor is:

📅MOE 2064

Q57.

Battery (12V) reads 11V on voltmeter due to:

📅MOE 2064

Q58.

Drift velocity (v_d) vs. electric field (E) relation obeying Ohm's law is:

📅MOE 2063

Q59.

Three equal resistors (R) forming an equilateral triangle have equivalent resistance between corners:

📅MOE 2066

Q60.

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 08

Q61.

The specific resistance of a wire 1.1 m long, 0.4 mm in diameter having a resistance of 0.42 ohm will be:

📅IOM 08

Q62.

A piece of wire of resistance 4 ohm is bent through 180° at midpoint and the two halves are twisted together. Their resistance is

📅IOM 04

Q63.

When 5.5 ohm and 4.5 ohm resistances are joined together in series and a 10 ohm resistance joined in parallel, the final resistance of the system is:

📅IOM 03

Q64.

Which of the following relations is called as current density?

📅IE-04

Q65.

A potentiometer consists of wire of length 4 m and resistance 10Ω. It is connected to a cell of emf 2V. The p.d. per unit length of the wire will be

📅IE-04

Q66.

The p.d. across a resistance is 12V. Internal resistance of cell is 0.02Ω delivering current is 10.4A, then e.m.f. of cell is

📅TE-05

Q67.

The equivalent resistance of network of three 4Ω resistors cannot be:

📅IE-07

Q68.

A meter of internal resistance R can measure a max. voltage of 10 mV. For it to measure a max. of 10V, we have to:

📅IE-01

Q69.

Two resistors are joined in parallel whose resultant is 6/5Ω. One of the resistance wire is broken and the effective resistance is 2Ω. The resistance of the wire that got broken was

📅MOE 2010

Q70.

What is the current supplied by the battery in the circuit shown in the figure?

📅BPKIHS-95

Q71.

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,

📅BPKIHS-97

Q72.

Potentiometer is a device based on the principle that potential difference across the potentiometer wire is:

📅BPKIHS 05

Q73.

There are two wires A and B. The radius of B is one fourth of A. Then ratio of resistance of B to A if both are of same material is

📅BPKIHS-06

Q74.

Which of the following quantities does not change when a resistor connected to a battery is heated due to current?

📅BPKIHS-97

Q75.

If the radius of a copper wire carrying a current is doubled, the drift velocity of electrons will

📅MOE 2010

Q76.

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

📅

Q77.

If a copper wire is stretched to make 0.1% thinner, then the percentage increase in resistance would be nearly

📅

Q78.

In a Wheatstone's bridge, the battery and galvanometer are interchanged, the condition for balance

📅

Q79.

When a potential difference is applied across a conductor, only the electron drift and current flowing is I. If the positive ion had also drifted, then the current would have been

📅

Q80.

Out of 3 equal resistances, how many different combinations are possible?

📅

Q81.

An external resistance R is connected to a cell of emf E and internal resistance r. The current in external circuit is maximum when

📅

Q82.

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

📅

Q83.

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

📅

Q84.

Three resistances 20Ω, 30Ω and 50Ω are connected in parallel and a potential difference of 20V is applied across the terminals of combination. The p.d. across 30Ω resistance is

📅

Q85.

A uniform wire of resistance R is divided into ten equal parts and all of them are connected in parallel. The equivalent resistance will be

📅

Q86.

Masses of three wires of same material are in the ratio of 1:2:3 and their lengths are in the ratio of 3:2:1. Electrical resistance of these wires will be in the ratio of

📅

Q87.

The resistance of a conductor is 5Ω at 50°C and 6Ω at 100°C. What is the resistance at 0°C?

📅

Q88.

The length of a conductor is halved, its conductivity will be

📅

Q89.

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.

📅

Q90.

Two wires of same dimensions but resistivities ρ₁ and ρ₂ are connected in series. The equivalent resistivity of the combination is

📅

Q91.

1 kg piece of copper is drawn into a wire 1mm thick and another piece into a wire 2mm thick. Compare the resistance of these wires

📅

Q92.

Two unequal resistances are connected in series with a cell. Which of the following statements is true?

📅

Q93.

Four wires each of 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

📅

Q94.

A primary cell of e.m.f 2 volt, when short circuited gives a current of 4A, its internal resistance in ohm will be

📅

Q95.

As shown in fig. below, the current flowing in the 2R resistor is

📅

Q96.

A battery is connected to an external circuit. The potential drop within the battery is proportional to

📅

Q97.

The e.m.f. of a generator is 6 volt and internal resistance is 0.5 kΩ. The reading of a voltmeter having an internal resistance of 2.5 kΩ is

📅

Q98.

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

📅

Q99.

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 p.d. of 15V, the e.m.f. of the battery is

📅

Q100.

A cell supplies a current I₁ through a resistance R₁ and a current I₂ through resistance R₂. The internal resistance of the cell is

📅

Q101.

Five cells each of internal resistance 0.2Ω and e.m.f. 2V are connected in series with a resistance of 4Ω. The current through the external resistance is

📅

Q102.

A battery is made by connecting 6 cells each having capacity 5Ah at 1.5 volt. The battery will have capacity equal to

📅

Q103.

Two identical cells send the same current in 3Ω resistance, whether connected in series or in parallel. The internal resistance of the cell should be

📅

Q104.

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

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Q105.

A battery of internal resistance r having no lead resistance, has an e.m.f E volt. What is the observed e.m.f. across the terminal of the battery when a load resistance R (= r) is connected to its terminals

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Q106.

A, B, C and D are four resistances of 2, 2, 2 and 3Ω respectively. They are used to from 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

📅

Q107.

Two cells having emf and internal resistance 10V, 5Ω and 6V, 3Ω are connected in series with unlike plate join together through a load of 2Ω. Then find p.d of each cell

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Q108.

Two cells of 10V, 5Ω and 6V, 3Ω are joined in series with like plates joined together through a load 2Ω. Then p.d. of each cell is

📅

Q109.

Two cells of equal emf E and different internal resistances r₁ and r₂ are connected in series through a variable load of R. Then value of R so that p.d. across first cell is zero

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Q110.

'n' identical cells each of emf 'E' and internal resistance 'r' are joined in series with two cells A and B are connected wrongly. Find The p.d. across A or B (n > 2)

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Q111.

24 cells each of 2V and 1Ω joined in mixed grouping through 6Ω. P_max and I_max will be

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Q112.

A battery is delivering a maximum power of 24 W in a load. The circuit is under maximum power condition and supplying a maximum current of 2A. Emf. and internal resistance of battery will be

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Q113.

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?

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Q114.

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?

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Q115.

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

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Q116.

Figure represents a part of closed circuit. The p.d. between points A and B (V_A - V_B) is

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Q117.

A battery of emf 10V is connected to resistance as shown in the figure. What is the potential difference between A and B?

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Q118.

For what value of unknown resistance x, the potential difference between B and D will be zero in the arrangement shown?

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Q119.

A uniform wire of resistance 36Ω is bent in the form of a circle. Then effective resistance across the points A and B is

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Q120.

A current of 1mA flows through a copper wire. How many electrons will pass a point in each second?

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Q121.

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

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Q122.

A wire has non-uniform cross-section. It carries a current I. The drift velocity of electrons

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Q123.

A potential difference 'V' is applied across a conductor having length 'l' and thickness 't'. If thickness is doubled then V will become/remains

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Q124.

What is the total momentum of electrons in the wire having 100m length and carrying 10A current.

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Q125.

A 10m long wire of resistance 20Ω is connected in series with a battery of e.m.f. 6 volts and a resistance of 10Ω. The potential gradient along the wire in volt per meter is

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Q126.

A cell can be balanced against 110 cm and 100 cm of potentiometer wire respectively when in open circuit and when short circuited through a resistance of 10Ω. Find the internal resistance of the cell

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Q127.

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 main cell used in potentiometer is

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Q128.

If the resistance of ammeter (R_A) is connected across the series and voltmeter of (R_V) across the parallel, then to measure the value of R:

📅KU 2016

Q129.

The radius of a conductor is doubled, resistance will be:

📅KU 2017

Q130.

The wire has resistance 32Ω. When its length is doubled, then percentage increase in resistance will be

📅IOM 2017

Q131.

The resistance of wire 40Ω. When it is bend through 180° and twisted together then new resistance will be

📅IOM 2017

37Electric current

Table 1: Electric Current Basics

Table 1: Charge Carriers in Different Media

Table 1: Current-Drift Relation

Table 1: Current Density

Table 1: Resistance and Resistivity

Table 2: Units

Table 1: Ohm's Law Points

Table 1: EMF of Cell

Table 2: EMF Independent Of

Table 1: Series, Parallel and Mixed Grouping of Identical Cells

Table 1: Wheatstone Bridge Points

Table 1: Potentiometer Formulae

Table 2: Potentiometer Properties

Table 1: Meter Bridge Formulae

Table 2: Meter Bridge Points

Table 1: Important Points

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