JEE Advanced PYQ Physics – Galvanometer, Ammeter and Voltmeter Conversion

Q 1 :

A moving coil galvanometer has 50 turns and each turn has an area $2 \times 10^{- 4} m^{2} .$ The magnetic field produced by the magnet inside the galvanometer is 0.02 T. The torsional constant of the suspension wire is $10^{- 4}$ $N m r a d^{- 1}$ . When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 rad. The resistance of the coil of the galvanometer is $50 Ω$ . This galvanometer is to be converted into an ammeter capable of measuring current in the range $0 - 1.0 A$ . For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ohms, is _______. [2018]

(5.56)

[ $Given: B = 0.02 T, C = 10^{- 4} {Nm rad}^{- 1}$

$θ = 0.2 rad$

$N = 50$ and

$A = 2 \times 10^{- 4} m^{2}$ ]

We know, $C θ = N B A I_{g}$

$∴$ $I_{g} = \frac{C θ}{N B A} = \frac{10^{- 4} \times 0.2}{50 \times 2 \times 10^{- 4} \times 0.02} = 0.1 A$

To convert a galvanometer to an ammeter, a shunt is used in parallel to the galvanometer.

$I_{g} \times G = (I - I_{g}) S$

$∴$ $S = \frac{I_{g} G}{I - I_{g}} = \frac{0.1 \times 50}{1 - 0.1} = \frac{50}{9} = 5.56 Ω$

Q 2 :

Two identical moving coil galvanometers have 10 resistance and full scale deflection at $2 μ A$ current. One of them is converted into a voltmeter of $100 mV$ full scale reading and the other into an ammeter of $1 mA$ full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm's law experiment with $R = 1000 Ω$ resistor by using an ideal cell. Which of the following statement(s) is(are) correct? [2019]

The resistance of the voltmeter will be $100 k$
The measured value of $R$ will be $978 < R < 982$
If the ideal cell is replaced by a cell having internal resistance of 5, then the measured value of $R$ will be more than 1000
The resistance of the ammeter will be 0.02 (round off to $2^{nd}$ decimal place).

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(2, 4)

$Here, G = 10 Ω, I_{g} = 2 \times 10^{- 6} A, V = 100 mV = 0.1 V, I = 10^{- 3} A$

Using, $V = I_{g} (G + R)$ [R = resistance connected in series with the galvanometer]

$\Rightarrow 0.1 = 2 \times 10^{- 6} R_{v}$

$∴$ $R_{v} = 5 \times 10^{4} Ω$ (Resistance of voltmeter)

Also, $I_{g} G = (I - I_{g}) S$

$2 \times 10^{- 6} \times 10 = (10^{- 3} - 2 \times 10^{- 6}) S$

$∴$ $S = 2 \times 10^{- 2} Ω$ (Resistance of ammeter)

$R_{A} = \frac{G S}{G + S} = \frac{10 \times 0.02}{10 + 0.02} \approx 0.02 Ω$

$I = \frac{E}{\frac{50, 000 \times 1000}{51000} + 0.02} = \frac{E}{980.41}$

$V_{a b} = \frac{E}{980.41} \times \frac{50, 000 \times 1000}{51000} = \frac{E}{980.41} \times 980.39$

$∴$ $R_{measured} = \frac{V_{a b}}{I} = \frac{\frac{E}{980.41} \times 980.39}{\frac{E}{980.41}} = 980.39 Ω$

If the voltmeter shows full-scale deflection, then

$0.1 = \frac{E}{980} \times (\frac{1000}{51000}) \times 5 \times 10^{4}$

$∴$ $E = 999.6 mV$

Since $i_{A} = 10^{- 3} A$

$∴$ $Maximum reading of R = \frac{999.6 \times 10^{- 3}}{1 \times 10^{- 3}} = 999.6 Ω$

Q 3 :

Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers $R_{c} < \frac{R}{2}$ , which of the following statement(s) about any one of the galvanometers is (are) true? [2016]

The maximum voltage range is obtained when all the components are connected in series.
The maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and the second galvanometer is connected in parallel to the first galvanometer.
The maximum current range is obtained when all the components are connected in parallel.
The maximum current range is obtained when the two galvanometers are connected in series and the combination is connected in parallel with both the resistors.

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Select one or more options

(1, 3)

The range of voltmeter

$V = I_{g} (R_{e q} + G)$

$∴$ Maximum voltage can be obtained if the equivalent resistance of components is maximum, i.e. when all the components are connected in series.

The range of ammeter

$I = I_{g} (1 + \frac{G}{S_{e q}})$

$∴$ Maximum current range can be obtained if the equivalent shunt resistance is minimum, i.e. when all the components are connected in parallel.

Q 4 :

Statement-1: The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.

Statement-2: Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized. [2008]

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
Statement-1 is True, Statement-2 is False
Statement-1 is False, Statement-2 is True

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(3)

Sensitivity of a moving coil galvanometer, $\frac{θ}{I} = \frac{N B A}{C}$

If $B$ increases by using an iron core, $\frac{θ}{I}$ i.e., sensitivity increases.

Soft iron can be easily magnetised and demagnetised.

Topic Question Set

Q 3 :

Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers $R_{c} < \frac{R}{2}$ , which of the following statement(s) about any one of the galvanometers is (are) true? [2016]

Q 4 :

Statement-1: The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.

Statement-2: Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized. [2008]

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Topic Question Set

Q 3 : Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers Rc<R2, which of the following statement(s) about any one of the galvanometers is (are) true? [2016]

Q 4 : Statement-1: The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil. Statement-2: Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized. [2008]

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Q 3 :

Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers $R_{c} < \frac{R}{2}$ , which of the following statement(s) about any one of the galvanometers is (are) true? [2016]

Q 4 :

Statement-1: The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.

Statement-2: Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized. [2008]