Question

Define current sensitivity of a galvanometer. “Increasing the current sensitivity may not necessarily increase the voltage sensitivity.” Give reason.

Hint:

Always remember: \[ \text{Voltage Sensitivity} = \frac{\text{Current Sensitivity}}{R} \] To improve voltage sensitivity, both current sensitivity should be high and resistance should be low.

Answer 1

Current Sensitivity: Current sensitivity of a galvanometer is defined as the deflection produced per unit current. Mathematically, \[ \text{Current Sensitivity} = \frac{\theta}{I} = \frac{n B A}{k} \] where \( \theta \) = deflection, \( I \) = current, \( n \) = number of turns, \( B \) = magnetic field, \( A \) = area of coil, \( k \) = torsional constant. Voltage Sensitivity: Voltage sensitivity is defined as the deflection per unit voltage: \[ \text{Voltage Sensitivity} = \frac{\theta}{V} = \frac{\theta}{IR} = \frac{1}{R} \cdot \frac{\theta}{I} \] \[ \Rightarrow \text{Voltage Sensitivity} = \frac{1}{R} \cdot \text{Current Sensitivity} \] where \( R \) is the resistance of the galvanometer coil. Reasoning: Even if current sensitivity increases, voltage sensitivity may not increase if the resistance \( R \) of the galvanometer also increases. For example, increasing the number of turns \( n \) increases both \( n \) and resistance \( R \). Thus, an increase in current sensitivity can be offset by a corresponding increase in resistance, resulting in no net gain or even a decrease in voltage sensitivity. % Final Answer Statement Answer: Increasing current sensitivity does not necessarily increase voltage sensitivity because voltage sensitivity also depends inversely on the resistance of the coil. If resistance increases along with current sensitivity, the overall voltage sensitivity may remain the same or decrease.