Match List-I with List-IIList-IList-II(Physical quantity)(Formula)(A)…

The correct answer is Option (3) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

In a moving coil galvanometer the deflection is \( \phi = (NAB/k)\,I \), where \( N \) is the number of turns, \( A \) the area of the coil, \( B \) the radial field and \( k \) the torsional constant of the spring. The two fields come from the Biot-Savart law and Ampere's circuital law.

(A) Current sensitivity of galvanometer — this matches (III) \( \displaystyle\frac{NAB}{k} \). The current sensitivity is the deflection per unit current, \( \phi/I = NAB/k \).

(B) Magnetic field at the centre of a circular coil — this matches (I) \( \displaystyle\frac{\mu_0 I}{2R} \). Every element of a loop of radius \( R \) is at distance \( R \) from the centre and perpendicular to it, so the Biot-Savart law adds up to \( \mu_0 I/(2R) \) for one turn.

(C) magnetic field due to a long straight wire carrying a current — this matches (IV) \( \displaystyle\frac{\mu_0 I}{2\pi R} \). Ampere's law on a circle of radius \( R \) round the wire gives \( B\,(2\pi R) = \mu_0 I \).

(D) Voltage sensitivity of galvanometer — this matches (II) \( \displaystyle\frac{NAB}{kR} \). The voltage sensitivity is the deflection per unit voltage; with \( V = IR \) for a coil of resistance \( R \), it is \( \phi/V = NAB/(kR) \).

NCERT (2026-27):
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),

    \( \displaystyle \frac{\phi}{V} = \left(\frac{NAB}{k}\right)\frac{I}{V} = \left(\frac{NAB}{k}\right)\frac{1}{R} \qquad (4.28) \)”