The AC voltage across a resistance can be measured using a:

The problem asks which instrument can measure an alternating-current (AC) voltage that appears across a pure resistance. To decide, we examine the working principle of each listed device, keeping in mind the special nature of AC signals.

First, recall that an AC quantity such as the current through the resistance can be written as $$i(t)=I_0\sin\omega t$$. The instantaneous value of $$i(t)$$ swings symmetrically above and below zero, so over a complete cycle the algebraic average of $$i(t)$$ itself is

$$\langle i(t)\rangle=\frac{1}{T}\int_0^T I_0\sin\omega t \,dt=0$$

However, the heating (thermal) effect of the current is determined by the mean square value, because the power converted to heat is

$$P=i^2 R$$

and the cycle average of $$i^2(t)$$ is

$$\langle i^2(t)\rangle=\frac{1}{T}\int_0^T I_0^2\sin^2\omega t\,dt=\frac{I_0^2}{2}=I_{\text{rms}}^2$$

So an instrument that depends on the heating effect of current will respond to $$I_{\text{rms}}$$ (and, correspondingly, to the rms value of the AC voltage across the resistance), whereas an instrument that attempts to respond to the instantaneous direction of the current will average out to zero.

Now we inspect each option.

Option A: Moving magnet galvanometer. A moving magnet or tangent galvanometer relies on the torque produced by a steady magnetic field generated by a direct current. Because the torque changes sign with the alternating direction of AC, the average torque over a cycle is zero, giving no deflection. Therefore, it cannot measure AC.

Option B: Moving coil galvanometer. A moving coil galvanometer (d'Arsonval type) likewise needs a unidirectional current through its coil. For an AC input $$i(t)=I_0\sin\omega t$$, the torque $$\tau\propto i(t)$$ changes sign every half cycle, again producing an average torque of zero. Hence, the pointer stays at rest and AC is not indicated.

Option C: Hot wire voltmeter. A hot wire voltmeter works on the principle that the wire’s expansion depends on the temperature rise caused by the heating power $$P=i^2R$$. As shown above, $$\langle i^2\rangle$$ is non-zero for AC; in fact it equals $$I_{\text{rms}}^2$$. Therefore the length of the hot wire (and thus the pointer reading) depends on the rms value of the alternating voltage, giving a correct measurement regardless of current direction. It can therefore measure AC as well as DC.

Option D: Potentiometer. A potentiometer is a null-balance device that compares an unknown emf to a known steady DC source. The balance condition requires a constant potential difference; if an AC source is connected, the potential difference reverses polarity, so balancing is impossible. Hence, a conventional potentiometer cannot measure AC.

From the above examination, only the hot wire voltmeter (Option C) operates on a principle—heating effect proportional to $$i^2$$—that yields a meaningful, non-zero indication for an AC voltage.

Hence, the correct answer is Option C.