Question

What should be the value of the inductance of the coil which is to be connected to \( 220 \, V, 50 \, Hz \) supply so that maximum current of \( 3\sqrt{2} \, A \) flows through the circuit?

• A. \( \left(\frac{22}{15}\right) H \)
• B. \( \left(\frac{15}{11\pi}\right) H \)
• C. \( \left(\frac{11}{15\pi}\right) H \)
• D. \( \left(\frac{22}{15}\sqrt{2}\right) H \)

Hint:

Always convert RMS values to peak values before applying AC formulas.

Answer 1

The Correct Option is C

Step 1: Relation for inductive circuit.
\[ I_0 = \frac{V_0}{\omega L} \]

Step 2: Convert RMS to maximum values.
\[ V_0 = \sqrt{2} \times 220 \]

Step 3: Given maximum current.
\[ I_0 = 3\sqrt{2} \]

Step 4: Angular frequency.
\[ \omega = 2\pi f = 2\pi \times 50 \]

Step 5: Substitute values.
\[ 3\sqrt{2} = \frac{220\sqrt{2}}{2\pi \cdot 50 \cdot L} \]

Step 6: Simplify.
\[ 3 = \frac{220}{100\pi L} \Rightarrow L = \frac{220}{300\pi} \]
\[ L = \frac{11}{15\pi} \]

Step 7: Final Answer.
\[ \boxed{\frac{11}{15\pi} \, H} \]