41Meters

📚
METERS
▢ Moving Coil Galvanometer:
❖ Use: Measurement of low current
❖ Construction:
  • •
    Rectangular coil
  • •
    Large number of turns
  • •
    Fine insulated copper wire
  • •
    Non-magnetic metallic frame
  • •
    Suspended by long thin phosphor bronze wire
  • •
    Placed between concave pole pieces of permanent magnet
  • •
    Soft cylindrical iron core produces radial magnetic field
  • •
    Mirror attached to suspension wire for lamp-scale reading
❖ Principle: Current-carrying coil placed in magnetic field experiences torque

Table 1: Moving Coil Galvanometer Formulae

Quantity
Formula / Meaning
Deflecting torque
\\\\\\\\(\\\\\\\\tau=BINA\\\\\\\\sin\\\\\\\\theta\\\\\\\\)
In radial field
\\\\\\\\(\\\\\\\\tau=BINA\\\\\\\\)
Restoring torque
\\\\\\\\(\\\\\\\\tau_r=C\\\\\\\\theta\\\\\\\\)
Equilibrium condition
\\\\\\\\(BINA=C\\\\\\\\theta\\\\\\\\)
Current
\\\\\\\\(I=\\\\\\\\frac{C}{BNA}\\\\\\\\theta\\\\\\\\)
Galvanometer constant
\\\\\\\\(K=\\\\\\\\frac{C}{BNA}\\\\\\\\)
Current-deflection relation
\\\\\\\\(I=K\\\\\\\\theta\\\\\\\\)
Deflection proportionality
\\\\\\\\(I\\\\\\\\propto\\\\\\\\theta\\\\\\\\)
❖ Symbols:
  • •
    \\\\\\\\(B\\\\\\\\) = magnetic field
  • •
    \\\\\\\\(I\\\\\\\\) = current
  • •
    \\\\\\\\(N\\\\\\\\) = number of turns
  • •
    \\\\\\\\(A\\\\\\\\) = area of coil
  • •
    \\\\\\\\(C\\\\\\\\) = restoring torque per unit twist
  • •
    \\\\\\\\(\\\\\\\\theta\\\\\\\\) = deflection / twist
❖ Sensitivity Increase:
  • •
    Increase area of moving coil
  • •
    Increase number of turns within limit
  • •
    Increase magnetic field \\\\\\\\(B\\\\\\\\)
  • •
    Use laminated ferro-cobalt steel permanent magnet
  • •
    Decrease torsional torque per unit twist \\\\\\\\(C\\\\\\\\)
▢ Current Sensitivity:
❖ Symbol: \\\\\\\\(I_s\\\\\\\\)
❖ Definition: Deflection produced in galvanometer when unit current flows through it

Table 1: Current Sensitivity

Quantity
Formula / Unit
Current sensitivity
\\\\\\\\(I_s=\\\\\\\\frac{\\\\\\\\theta}{I}\\\\\\\\)
Formula
\\\\\\\\(I_s=\\\\\\\\frac{NBA}{C}\\\\\\\\)
Unit
\\\\\\\\(rad\\\\\\\\ A^{-1}\\\\\\\\) or \\\\\\\\(division\\\\\\\\ A^{-1}\\\\\\\\)
Increased by
Increasing \\\\\\\\(B,N,A\\\\\\\\) or decreasing \\\\\\\\(C\\\\\\\\)
▢ Voltage Sensitivity:
❖ Symbol: \\\\\\\\(V_s\\\\\\\\)
❖ Definition: Deflection produced in galvanometer when unit voltage is applied across its terminals

Table 1: Voltage Sensitivity

Quantity
Formula / Unit
Voltage sensitivity
\\\\\\\\(V_s=\\\\\\\\frac{\\\\\\\\theta}{V}\\\\\\\\)
Formula
\\\\\\\\(V_s=\\\\\\\\frac{NBA}{CR}\\\\\\\\)
Unit
\\\\\\\\(rad\\\\\\\\ V^{-1}\\\\\\\\) or \\\\\\\\(division\\\\\\\\ V^{-1}\\\\\\\\)
Relation
\\\\\\\\(I_s=V_sR\\\\\\\\)
▢ Tangent Galvanometer:
❖ Principle: Based on tangent law

Table 1: Tangent Galvanometer

Point
Answer
Current relation
\\\\\\\\(I=K\\\\\\\\tan\\\\\\\\theta\\\\\\\\)
\\\\\\\\(K\\\\\\\\)
Galvanometer constant
Sensitivity
Smaller \\\\\\\\(K\\\\\\\\) gives larger sensitivity
Deflection relation
\\\\\\\\(I\\\\\\\\propto\\\\\\\\tan\\\\\\\\theta\\\\\\\\)
Most accurate deflection
\\\\\\\\(45^\\\\\\\\circ\\\\\\\\)
Reason
Variation of \\\\\\\\(\\\\\\\\tan\\\\\\\\theta\\\\\\\\) is maximum near \\\\\\\\(45^\\\\\\\\circ\\\\\\\\)
Best method to increase sensitivity
Increase external magnetic field
Position of coil
Placed in magnetic meridian
Purpose of magnetic meridian
To produce magnetic field at right angle to earth's field
▢ Ballistic Galvanometer:
❖ Use: Measures total charge passed through it for short duration

Table 1: Ballistic Galvanometer

Quantity
Formula / Point
Charge
\\\\\\\\(q=K\\\\\\\\theta_0\\\\\\\\)
Proportionality
\\\\\\\\(q\\\\\\\\propto\\\\\\\\theta_0\\\\\\\\)
\\\\\\\\(K\\\\\\\\)
Ballistic galvanometer constant
\\\\\\\\(\\\\\\\\theta_0\\\\\\\\)
First throw / initial deflection
Coil frame
Non-metallic frame
▢ Ammeter:
❖ Definition: Low resistance galvanometer used to measure current in a circuit
❖ Connection: Connected in series with circuit
❖ Reason for Series Connection: To avoid division of current
❖ Problem in Series: It slightly increases circuit resistance and decreases current being measured
❖ Ideal Ammeter: Zero resistance
❖ Conversion: Galvanometer is converted into ammeter by connecting low resistance shunt in parallel

Table 1: Ammeter Conversion Formulae

Quantity
Formula / Meaning
Shunt resistance
\\\\\\\\(S=\\\\\\\\frac{I_g}{I-I_g}G\\\\\\\\)
Using relative change in current
\\\\\\\\(S=\\\\\\\\frac{G}{n-1}\\\\\\\\)
Relative change
\\\\\\\\(n=\\\\\\\\frac{I}{I_g}\\\\\\\\)
\\\\\\\\(I_g\\\\\\\\)
Current for full scale deflection of galvanometer
\\\\\\\\(I\\\\\\\\)
Current to be measured
\\\\\\\\(G\\\\\\\\)
Resistance of galvanometer
❖ Important Points:
  • •
    Range of ammeter can be increased but cannot be decreased using shunt
  • •
    Increasing range of ammeter decreases resistance
  • •
    Ammeter of lower range has higher resistance than ammeter of higher range
  • •
    Resistance order: Microammeter > Milliammeter > Ammeter
❖ Uses of Shunt:
  • •
    Protects galvanometer/ammeter from strong current
  • •
    Converts galvanometer into ammeter
  • •
    Bypasses excess current through low resistance path
▢ Voltmeter:
❖ Definition: Instrument used to measure potential difference between two points in a circuit
❖ Connection: Connected in parallel with circuit
❖ Ideal Voltmeter: Infinite resistance
❖ Conversion: Galvanometer is converted into voltmeter by connecting high resistance in series

Table 1: Voltmeter Conversion Formulae

Quantity
Formula / Meaning
Series resistance
\\\\\\\\(R=\\\\\\\\frac{V}{I_g}-G\\\\\\\\)
Using relative change in voltage
\\\\\\\\(R=G(n-1)\\\\\\\\)
Relative change
\\\\\\\\(n=\\\\\\\\frac{V}{V_g}\\\\\\\\)
\\\\\\\\(V\\\\\\\\)
Voltage to be measured
\\\\\\\\(I_g\\\\\\\\)
Current for full scale deflection
\\\\\\\\(G\\\\\\\\)
Resistance of galvanometer
❖ Important Points:
  • •
    Range of voltmeter can be increased by adding high resistance in series
  • •
    Increasing range of voltmeter increases resistance
  • •
    Voltmeter of lower range has lower resistance than voltmeter of higher range
  • •
    Resistance order: Voltmeter > Millivoltmeter > Microvoltmeter
  • •
    Net resistance of voltmeter should be large so that it does not change potential difference
▢ Electrometer:
❖ Use: Measures potential difference very accurately
❖ Reason: Does not draw current
❖ Nature: Ideal voltmeter
▢ Resistance Order of Instruments:

Table 1: Instrument Resistance Order

Order
Relation
General
Voltmeter > Galvanometer > Ammeter
Ammeter range
Microammeter > Milliammeter > Ammeter
Voltmeter range
Voltmeter > Millivoltmeter > Microvoltmeter
Ideal ammeter
\\\\\\\\(R=0\\\\\\\\)
Ideal voltmeter
\\\\\\\\(R=\\\\\\\\infty\\\\\\\\)
▢ Instrument Deflection Relations:

Table 1: Deflection Relations

Instrument
Relation
Moving coil galvanometer
\\\\\\\\(I\\\\\\\\propto\\\\\\\\theta\\\\\\\\)
Tangent galvanometer
\\\\\\\\(I\\\\\\\\propto\\\\\\\\tan\\\\\\\\theta\\\\\\\\)
Ballistic galvanometer
\\\\\\\\(q\\\\\\\\propto\\\\\\\\theta_0\\\\\\\\)
Hot wire ammeter
\\\\\\\\(\\\\\\\\theta\\\\\\\\propto I^2\\\\\\\\)
▢ Read and Digest:

Table 1: Important Points

Fact
Answer
Moving coil galvanometer
Measures low current
Working principle of MCG
Current-carrying coil in magnetic field experiences torque
Torque in MCG
\\\\\\\\(\\\\\\\\tau=BINA\\\\\\\\sin\\\\\\\\theta\\\\\\\\)
Torque in radial field
\\\\\\\\(\\\\\\\\tau=BINA\\\\\\\\)
Restoring torque
\\\\\\\\(\\\\\\\\tau_r=C\\\\\\\\theta\\\\\\\\)
MCG current relation
\\\\\\\\(I=\\\\\\\\frac{C}{BNA}\\\\\\\\theta\\\\\\\\)
Current sensitivity
\\\\\\\\(I_s=\\\\\\\\frac{NBA}{C}\\\\\\\\)
Voltage sensitivity
\\\\\\\\(V_s=\\\\\\\\frac{NBA}{CR}\\\\\\\\)
Sensitivity of MCG increased by
Decreasing couple per unit twist / suspension
Tangent galvanometer principle
Tangent law
Tangent galvanometer current
\\\\\\\\(I=K\\\\\\\\tan\\\\\\\\theta\\\\\\\\)
Tangent galvanometer most accurate
\\\\\\\\(45^\\\\\\\\circ\\\\\\\\)
Best method to increase TG sensitivity
Increase external magnetic field
Ballistic galvanometer
Measures charge
Ballistic relation
\\\\\\\\(q=K\\\\\\\\theta_0\\\\\\\\)
Galvanometer to ammeter
Low resistance shunt in parallel
Ammeter connection
Series
Ideal ammeter resistance
Zero
Galvanometer to voltmeter
High resistance in series
Voltmeter connection
Parallel
Ideal voltmeter resistance
Infinity
Ammeter range increase
Resistance decreases
Voltmeter range increase
Resistance increases
Electrometer
Ideal voltmeter; draws no current
Deflection in MCG
Directly proportional to number of turns in coil
▢ High-Yield Recall:

Table 1: Meters One-Liners

Fact
Answer
Moving coil galvanometer use
Low current measurement
MCG principle
Torque on current-carrying coil
Deflecting torque
\\\\\\\\(\\\\\\\\tau=BINA\\\\\\\\sin\\\\\\\\theta\\\\\\\\)
Radial field torque
\\\\\\\\(\\\\\\\\tau=BINA\\\\\\\\)
Restoring torque
\\\\\\\\(\\\\\\\\tau_r=C\\\\\\\\theta\\\\\\\\)
MCG equilibrium
\\\\\\\\(BINA=C\\\\\\\\theta\\\\\\\\)
Current in MCG
\\\\\\\\(I=\\\\\\\\frac{C}{BNA}\\\\\\\\theta\\\\\\\\)
Galvanometer constant
\\\\\\\\(K=\\\\\\\\frac{C}{BNA}\\\\\\\\)
MCG relation
\\\\\\\\(I\\\\\\\\propto\\\\\\\\theta\\\\\\\\)
Current sensitivity
\\\\\\\\(I_s=\\\\\\\\frac{\\\\\\\\theta}{I}=\\\\\\\\frac{NBA}{C}\\\\\\\\)
Voltage sensitivity
\\\\\\\\(V_s=\\\\\\\\frac{\\\\\\\\theta}{V}=\\\\\\\\frac{NBA}{CR}\\\\\\\\)
Sensitivity increase
Increase \\\\\\\\(B,N,A\\\\\\\\); decrease \\\\\\\\(C\\\\\\\\)
Tangent galvanometer
\\\\\\\\(I=K\\\\\\\\tan\\\\\\\\theta\\\\\\\\)
TG most accurate deflection
\\\\\\\\(45^\\\\\\\\circ\\\\\\\\)
Ballistic galvanometer use
Charge measurement
Ballistic relation
\\\\\\\\(q=K\\\\\\\\theta_0\\\\\\\\)
Ammeter
Low resistance galvanometer
Ammeter connection
Series
Ideal ammeter
Zero resistance
Ammeter conversion
Shunt in parallel
Shunt formula
\\\\\\\\(S=\\\\\\\\frac{I_g}{I-I_g}G\\\\\\\\)
Shunt using \\\\\\\\(n\\\\\\\\)
\\\\\\\\(S=\\\\\\\\frac{G}{n-1}\\\\\\\\)
Voltmeter
Measures potential difference
Voltmeter connection
Parallel
Ideal voltmeter
Infinite resistance
Voltmeter conversion
High resistance in series
Series resistance for voltmeter
\\\\\\\\(R=\\\\\\\\frac{V}{I_g}-G\\\\\\\\)
Voltmeter resistance using \\\\\\\\(n\\\\\\\\)
\\\\\\\\(R=G(n-1)\\\\\\\\)
Resistance order
Voltmeter > Galvanometer > Ammeter
Ammeter range increase
Resistance decreases
Voltmeter range increase
Resistance increases
Electrometer
Ideal voltmeter
Q1.
An ammeter of range 1A has a resistance 0.9Ω. To extend the range to 10A, the necessary shunt required is: [BP 2014]
📅BP 2014
Q2.
An ammeter shows a current flowing through it. Now if an equal resistance to ammeter is joined parallel then [BP 2011]
📅BP 2011
Q3.
A galvanometer of internal resistance 10Ω needs 10-3 A for full scale deflection. The shunt resistance required for measurement is [MOE 2011]
📅MOE 2011
Q4.
A galvanometer can be converted to a voltmeter by connecting [KU 2012]
📅KU 2012
Q5.
A potentiometer consists of wire of length 4m 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]
📅IE-04
Q6.
The sensitivity of moving coil depends on: [IE-08]
📅IE-08
Q7.
A galvanometer shows full scale deflection when a current of 2mA flows through it. If the resistance of galvanometer is 100Ω, what is the range of voltmeter without adding high resistance in series?
Q8.
Which of the following is likely to have largest resistance? [BPKIHS-07]
📅BPKIHS-07
Q9.
Ten identical cells each of emf ε and internal resistance r are connected in series to form a closed circuit. An ideal voltmeter connected across three cells will read: [BPKIHS-08]
📅BPKIHS-08
Q10.
A moving coil galvanometer has a resistance of 900Ω. In order to send only 10% of the main current through this galvanometer, the resistance of the required shunt is: [BPKIHS-08]
📅BPKIHS-08
Q11.
A galvanometer of resistance 20Ω gives full scale deflection when a current of 0.01A is passed through it. It is desired to convert it into an ammeter reading 20A in full scale. The only shunt available is 0.05Ω. The resistance that must be connected in series with the coil of the galvanometer is [BPKIHS-09]
📅BPKIHS-09
Q12.
An ammeter having resistance 10Ω allows a current of 0.002A to flow through it. For it to allow a current of 2A, we should: [BPKIHS 01]
📅BPKIHS 01
Q13.
To convert a galvanometer into an ammeter: [BPKIHS 2005/2017]
📅BPKIHS 2005•BPKIHS 2017
Q14.
The resistance of a voltmeter should be large to ensure that [BPKIHS-97]
📅BPKIHS-97
Q15.
A meter of internal resistance R can measure a max. voltage of 10mV. For it to measure a max. of 10V, we have to: [IE-01]
📅IE-01
Q16.
Which has greater resistance?
Q17.
The deflection in a galvanometer falls from 50 divisions to 20 when a 12 ohm shunt is applied. The galvanometer resistance is
Q18.
A galvanometer of resistance 5 ohms gives full scale deflection for a potential difference of 10mV. To convert the galvanometer into a voltmeter giving a full scale deflection for a potential difference of 1V, the size of the resistance that must be attached to the voltmeter is
Q19.
The deflection in moving coil galvanometer is reduced to half, when it is shunted with a 40Ω coil. The resistance of the galvanometer is
Q20.
A voltmeter with a resistance of 50×103Ω is used to measure voltage in a circuit. To increase its range to 3 times, the additional resistance to be put in series is
Q21.
An ammeter has a resistance R0 and range I. Which of the following resistance can be connected in series with it to decrease its range to I/n?
Q22.
A milliammeter of resistance 8Ω gives a full scale deflection for a current of 25mA. If it is used as a voltmeter, it will give a full scale deflection for a potential difference of
Q23.
A voltmeter of resistance of 50×103Ω is used to measure voltage in a circuit. To increase its range to 3 times, the additional resistance to be put in series is
Q24.
A moving coil galvanometer has a resistance of 90Ω. If only 10% of the main current may flow through the galvanometer, in what way and which resistance is to be used?
Q25.
A voltmeter has resistance of 2000Ω and it can measure up to 2V. If we want to increase its range by 8V, then required resistance in series will be
Q26.
If only 2% of the main current is to be passed through a galvanometer of resistance G, then the resistance of shunt will be
Q27.
A galvanometer of resistance 10Ω gives a full scale deflection when a current of 0.04A is passed through it. It is desired to convert it into an ammeter reading 10A in full scale. The only shunt available is 0.06Ω. The resistance that must be connected in series with the coil of the galvanometer is