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Formulas/physics/Moving Charges/Current Sensitivity of Galvanometer

Current Sensitivity of Galvanometer

Deflection per unit current. Increased by larger N, B, A or weaker spring k. Voltage sensitivity = S_I / G where G is galvanometer resistance.
Class 12
Derivation

Definition

Current sensitivity is the deflection per unit current:

SI=αI=NBAk\boxed{S_I = \frac{\alpha}{I} = \frac{NBA}{k}}

Units: rad A−1^{-1} or div A−1^{-1}.

Maximising Current Sensitivity

Increase NN, BB, AA or decrease kk.

Voltage Sensitivity

SV=αV=αIG=SIG=NBAkGS_V = \frac{\alpha}{V} = \frac{\alpha}{IG} = \frac{S_I}{G} = \frac{NBA}{kG}

The Trade-off

Increasing NN increases SIS_I but also increases GG (more wire → more resistance). The effect on SVS_V:

SV=NBAkG∝NGS_V = \frac{NBA}{kG} \propto \frac{N}{G}

Since G∝NG \propto N (resistance proportional to length of wire), SV∝N/N=constantS_V \propto N/N = \text{constant}.

Increasing NN alone does not improve voltage sensitivity.

Note
A galvanometer with high current sensitivity is not necessarily a good voltmeter. For voltage measurement, high $G$ is actually desirable — it minimises current drawn from the circuit.