Question

A current of 200 $\mu A$ deflects the coil of a moving coil galvanometer through $60^{\circ}$. The current to cause deflection through $\frac{\pi}{10}$ radian is :

• A. 30 $\mu A$
• B. 120 $\mu A$
• C. 60 $\mu A$
• D. 180 $\mu A$

Answer 1

The Correct Option is C

The solution to this problem necessitates an understanding of the operational principle of a moving coil galvanometer. In such a device, the deflection is directly proportional to the current passing through it, a phenomenon rooted in the principle that torque on a coil within a magnetic field is proportional to both the current and the coil's number of turns.

The deflection is mathematically represented as:

\(\theta \propto I\)

Given data:

• A current of 200 \(\mu A\) results in a deflection of \(60^{\circ}\).
• The objective is to determine the current that produces a deflection of \(\frac{\pi}{10}\) radians.

Firstly, convert the given angle from degrees to radians:

\(60^{\circ} = \frac{60 \times \pi}{180} = \frac{\pi}{3} \text{ radians}\)

Utilizing the proportionality, establish equations for both given scenarios:

\(\frac{\pi}{3} \propto 200 \mu A\)

\(\frac{\pi}{10} \propto I_{\text{required}}\)

Since the proportionality constant remains constant, equate the ratios:

\(\frac{200}{I_{\text{required}}} = \frac{\frac{\pi}{3}}{\frac{\pi}{10}}\)

Simplify the right side of the equation:

\(\frac{\pi}{3} \cdot \frac{10}{\pi} = \frac{10}{3}\)

The equation is now:

\(\frac{200}{I_{\text{required}}} = \frac{10}{3}\)

Solve for \(I_{\text{required}}\) by cross-multiplication:

\(I_{\text{required}} = \frac{200 \times 3}{10} = 60 \mu A\)

Consequently, the current necessary to achieve a deflection of \(\frac{\pi}{10}\) radians is 60 \(\mu A\).

The correct option corresponds to 60 \(\mu A\).