Given:
- \( i_2 = 200 \, \mu A \),
- \( \theta_2 = 60^\circ = \frac{\pi}{3} \, \text{radians} \).
The deflection \( \theta \) is proportional to the current \( i \). Therefore:
\(\frac{i_1}{i_2} = \frac{\theta_1}{\theta_2}.\)
For \( \theta_1 = \frac{\pi}{10} \, \text{radians} \):
\(\frac{i_1}{200} = \frac{\frac{\pi}{10}}{\frac{\pi}{3}}.\)
Simplify:
\(\frac{i_1}{200} = \frac{3}{10} \implies i_1 = 200 \times \frac{3}{10} = 60 \, \mu A.\)
The Correct answer is: 60 $\mu A$
Galvanometer:
A galvanometer is an instrument used to show the direction and strength of the current passing through it. In a galvanometer, a coil placed in a magnetic field experiences a torque and hence gets deflected when a current passes through it.
The name "galvanometer" is derived from the surname of Italian scientist Luigi Galvani, who in 1791 discovered that electric current makes a dead frog’s leg jerk.
A spring attached to the coil provides a counter torque. In equilibrium, the deflecting torque is balanced by the restoring torque of the spring, and we have the relation:
\[ NBAI = k\phi \]
Where:
As the current \( I_g \) that produces full-scale deflection in the galvanometer is very small, the galvanometer alone cannot be used to measure current in electric circuits.
To convert a galvanometer into an ammeter (to measure larger currents), a small resistance called a shunt is connected in parallel to the galvanometer.
To convert it into a voltmeter (to measure potential difference), a high resistance is connected in series with the galvanometer.