Read the following passage and answer the questions.
A school laboratory has a moving coil galvanometer. Its rectangular coil has 100 turns, and each turn has an area of 4.0 cm2. The coil can turn between the curved pole pieces of a magnet, with a soft iron cylinder inside it. The magnetic field at the coil is 0.25 T. A spring gives a restoring torque of \(2.0\times10^{-5}\ \mathrm{N\,m}\) for each radian of twist. The coil has a resistance of 50 Ω. The pointer reaches the end of the scale for a current of 2 mA. A student first uses the galvanometer as a current detector in a Wheatstone bridge. Later she plans to change it into an ammeter and into a voltmeter, so that she can measure larger currents and voltages in other circuits.
Consider the following statements about changing the galvanometer into a voltmeter:
(A) The voltmeter is connected in series with the resistor whose voltage is to be measured.
(B) A large resistance is connected in series with the coil of the galvanometer.
(C) If the coil is rewound with twice as many turns of the same wire, keeping its area the same, the voltage sensitivity doubles.
(D) The voltmeter draws only a very small current from the circuit.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (D) only
A voltmeter measures the voltage across a part of a circuit. It must disturb that part as little as possible.
(A) The voltmeter is connected in series with the resistor whose voltage is to be measured. — False. A voltmeter is connected in parallel with the section whose voltage it measures.
(B) A large resistance is connected in series with the coil of the galvanometer. — True. The large series resistance \( R \) makes the resistance of the voltmeter \( R_G+R\simeq R \), which is large.
(C) If the coil is rewound with twice as many turns of the same wire, keeping its area the same, the voltage sensitivity doubles. — False. Doubling \( N \) doubles the current sensitivity \( NAB/k \). The wire also becomes twice as long, so the resistance doubles too. The voltage sensitivity \( NAB/kR \) then stays the same.
(D) The voltmeter draws only a very small current from the circuit. — True. Because of its large resistance, very little current is taken from the circuit. So the voltage being measured hardly changes.
NCERT (2026-27):
The Moving Coil Galvanometer – “… For this it must be connected in parallel with that section of the circuit. Further, it must draw a very small current, otherwise the voltage measurement will disturb the original set up by an amount which is very large. … To ensure this, a large resistance R is connected in series with the galvanometer.”
The Moving Coil Galvanometer – “Thus, the current sensitivity doubles. However, the resistance of the galvanometer is also likely to double, since it is proportional to the length of the wire. … thus the voltage sensitivity, … remains unchanged.”