This question was previously asked in

SSC JE EE Previous Year Paper 6 (Held On: 25 Jan 2018 Morning)

Option 1 : 5

ME Subject Test 1: Strength of Materials

9153

20 Questions
20 Marks
18 Mins

**Concept:**

Operating torque:

In moving iron instruments, the deflecting torque is given by

\(\Rightarrow \theta = \dfrac{1}{2}\dfrac{{{I^2}}}{{{K_c}}}\dfrac{{dL}}{{d\theta }}\)

I is the operating current in Ampere

L is the inductance in Henry

θ is the deflection angle in radians

Deflection is directly proportional to the square of the RMS value of the operating current. Hence, this instrument possesses high operating torque.

**Calculation:**

\(\begin{array}{l} L = \left( {20 + 4\;\theta } \right)\;\mu H\\ \frac{{dL}}{{d\theta }} = 4\;\mu H/rad \end{array}\)

\(\begin{array}{l} \theta = \frac{1}{2}\frac{{{I^2}}}{{{K_c}}}\frac{{dL}}{{d\theta }}\\ \theta = \frac{1}{2} \times \frac{{{{\left( 5 \right)}^2}}}{{10 \times {{10}^{ - 6}}}} \times \left( 4 \right) \times {10^{ - 6}}\\ \Rightarrow \;\theta = 5\;rad \end{array}\)