Question

Define current sensitivity and voltage sensitivity of a galvanometer. Increasing the current sensitivity may not necessarily increase the voltage sensitivity of a galvanometer. Justify.

Answer 1

Hint: Galvanometer is used to detect current in a circuit. Current sensitivity determines how much a galvanometer will deflect on passing some current through it. Similarly, voltage sensitivity determines how much the galvanometer will undergo deflection when some potential difference is applied across its ends.

Formula used: $$I_s={\displaystyle \frac{\theta }{I}}={\displaystyle \frac{nBA}{c}}$$
 $$V_s={\displaystyle \frac{nBA}{cR}}$$

Complete step by step answer:
Current sensitivity is defined as the deflection caused in the galvanometer per unit flow of current. It is given by-
 $$I_s={\displaystyle \frac{\theta }{I}}={\displaystyle \frac{nBA}{c}}$$ ----- (1)
Here, $$\theta$$ is the angle by which galvanometer needle gets deflected
 $$I$$ is the current flowing through the galvanometer
 $$n$$ is the number of turns in the coil of the galvanometer
 $$B$$ is a magnetic field around the coil.
 $$A$$ is area of cross section of the coil
 $$c$$ is the restoring torque per unit twist
 Voltage sensitivity is defined as deflection caused in the galvanometer when a unit potential difference is applied across it.
It is given by-
 $$V_s={\displaystyle \frac{\theta }{V}}={\displaystyle \frac{\theta }{IR}}$$ ---- (2)
Here, $$V$$ is the potential drop
 $$R$$ is the resistance
From eq (1) and eq (2), we get,
 $$V_s={\displaystyle \frac{nBA}{cR}}$$
 So, the current sensitivity is $$I_s={\displaystyle \frac{\theta }{I}}={\displaystyle \frac{nBA}{c}}$$ and the voltage sensitivity is $$V_s={\displaystyle \frac{nBA}{cR}}$$
As we can see, voltage sensitivity depends on current sensitivity as well as resistance. So, if we increase current sensitivity, resistance may or may not vary. For example- if we increase current sensitivity by increasing the number of turns in the coil, the resistance will also increase. Hence, the voltage sensitivity may not be affected in this case. If the current sensitivity and resistance increase or decrease in the same ratio there will be no change in voltage sensitivity.

Therefore, the current sensitivity may not necessarily increase the voltage sensitivity of a galvanometer.

Note: Galvanometer is a device that is used to detect current in a circuit. It can be modified to act like an ammeter or voltmeter. When current flows through the coil of the galvanometer, a force acts on it due to which the coil is twisted and causes the needle of the galvanometer to deflect.