Match List-I with List-II in the context of a Moving Coil Galvanometer of \( N \) closely wound turns, consisting of coil area \( A \), spring torsional constant \( k \), carrying a current \( I \), placed in a magnetic field \( B \). \( R \) is a large resistance connected in series with the Galvanometer.
| List-I | List-II | ||
| Physical Quantity | Mathematical expression | ||
| (A) | Magnetic torque | (I) | \( (NAB)k^{-1} \) |
| (B) | Angular deflection | (II) | \( (NAB)k^{-1}R^{-1} \) |
| (C) | Current sensitivity | (III) | \( NIAB \) |
| (D) | Voltage sensitivity | (IV) | \( (NABk^{-1})I \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
In a moving coil galvanometer the magnetic torque on the coil is balanced by the restoring torque of the spring, \( k\phi \), at the steady deflection \( \phi \).
(A) Magnetic torque — this matches (III) \( NIAB \). In a radial field the plane of the coil stays parallel to the field, so the torque on the N-turn coil is always \( NIAB \).
(B) Angular deflection — this matches (IV) \( (NABk^{-1})I \). At equilibrium the two torques balance.
\( k\phi = NIAB \ \Rightarrow\ \phi = (NAB/k)\,I \)
(C) Current sensitivity — this matches (I) \( (NAB)k^{-1} \). Current sensitivity is the deflection per unit current.
\( \phi/I = NAB/k \)
(D) Voltage sensitivity — this matches (II) \( (NAB)k^{-1}R^{-1} \). Voltage sensitivity is the deflection per unit voltage, and with the resistance R in the circuit \( V = IR \).
\( \phi/V = \phi/(IR) = NAB/(kR) \)
NCERT (2026-27):
The Moving Coil Galvanometer – “… The magnetic torque NIAB tends to rotate the coil. A spring Sp provides a counter torque \( k\phi \) that balances the magnetic torque NIAB; resulting in a steady angular deflection \( \phi \). In equilibrium
\( \displaystyle k\phi = NI AB \)
where k is the torsional constant of the spring; i.e. the restoring torque per unit twist. The deflection \( \phi \) is indicated on the scale by a pointer attached to the spring. We have
\( \displaystyle \phi = \left(\frac{NAB}{k}\right) I \qquad (4.26) \)”
The Moving Coil Galvanometer – “… We define the current sensitivity of the galvanometer as the deflection per unit current. From Eq. (4.26) this current sensitivity is,
\( \displaystyle \frac{\phi}{I} = \frac{NAB}{k} \qquad (4.27) \)”
The Moving Coil Galvanometer – “… We define the voltage sensitivity as the deflection per unit voltage. From Eq. (4.26),
\( \displaystyle \frac{\phi}{V} = \left(\frac{NAB}{k}\right)\frac{I}{V} = \left(\frac{NAB}{k}\right)\frac{1}{R} \qquad (4.28) \)”