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.
The student replaces the spring with a stiffer one, which gives a larger restoring torque for each radian of twist. Compared with the old graph of deflection \(\phi\) against current \(I\), the new graph is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → a straight line through the origin with a smaller slope
The radial field keeps the magnetic torque equal to \( NIAB \) at every position of the coil. At the steady deflection, the spring torque \( k\phi \) balances it.
\( \begin{aligned} k\phi &= NIAB \\ \phi &= \left(\frac{NAB}{k}\right)I \end{aligned} \)
So the graph of \( \phi \) against \( I \) is a straight line through the origin, and its slope is \( NAB/k \). A stiffer spring has a larger \( k \).
Option (1) a straight line through the origin with a larger slope — Incorrect. A larger \( k \) makes \( NAB/k \) smaller. The slope becomes larger only for a softer spring.
Option (2) a straight line through the origin with a smaller slope — Correct. With a larger \( k \), each current gives a smaller deflection. The line still starts at the origin, so only its slope falls.
Option (3) a curve through the origin whose slope decreases as \(I\) increases — Incorrect. A bending graph would need a torque that changes as the coil turns. In the radial field the torque stays \( NIAB \), so the graph stays straight.
Option (4) the same straight line as before — Incorrect. The deflection is set by the balance of the two torques. Changing the spring changes \( k \), so the line cannot stay the same.
NCERT (2026-27):
The Moving Coil Galvanometer – “… There is a cylindrical soft iron core which not only makes the field radial but also increases the strength of the magnetic field. …”
The Moving Coil Galvanometer – “… The deflection φ is indicated on the scale by a pointer attached to the spring. We have”
\( \displaystyle \phi=\left(\frac{NAB}{k}\right)I \)\( \qquad (4.26) \)