Correct Answer - Option 2 : 40%
CONCEPT:
Galvanometer:
- A galvanometer is a device that is used to detect the current, to find the direction of the current, and also to compare the current.
Current sensitivity of a galvanometer:
- The deflection θ per unit current is known as the current sensitivity of the galvanometer.
Voltage sensitivity of a galvanometer:
- The deflection θ per unit voltage is known as the voltage sensitivity of the galvanometer.
CALCULATION:
- We know that the voltage sensitivity is given as,
\(⇒ V_{s}=\left ( \frac{I_{s}}{R} \right )\) -----(1)
Where Vs = voltage sensitivity, Is = current sensitivity, and R = resistance
- When the resistance is increased by factor 2,
\(⇒ R^{'}=2R\) -----(2)
\(⇒ I_{s}^{'}=\) Is + 20% of Is
\(⇒ I_{s}^{'}=I_{s}+\frac{20}{100}I_{s}\)
\(⇒ I_{s}^{'}=1.2I_{s}\) -----(3)
\(⇒ V_{s}^{'}=\frac{I_{s}^{'}}{R^{'}}\)
\(⇒ V_{s}^{'}=\frac{1.2I_{s}}{2R}\) -----(4)
By equation 1 and equation 4,
\(⇒ V_{s}^{'}=0.6V_{s}\) -----(5)
- The change in voltage sensitivity is given as,
⇒ %\( \Delta V=\frac{V_{s}^{'}-V_{s}}{V_{s}}\times100\)
⇒ %\( \Delta V=\frac{0.6V_{s}-V_{s}}{V_{s}}\times100\)
⇒ %\( \Delta V=-40\)%
Hence, option 2 is correct.