Question

A \(70\,\text{mH}\) inductor is connected to \(220\,\text{V},\ 50\,\text{Hz}\) AC supply. The rms value of the current in the circuit is:

• A. \(\dfrac{100}{\sqrt{2}\pi}\,\text{A}\)
• B. \(10\,\text{A}\)
• C. \(\dfrac{50}{\pi}\,\text{A}\)
• D. \(\dfrac{10\sqrt{2}}{\pi}\,\text{A}\)

Hint:

For a pure inductor in AC circuit: \[ X_L=2\pi fL \] and \[ I_{\text{rms}}=\frac{V_{\text{rms}}}{X_L}. \]

Answer 1

The Correct Option is B

Step 1: Recall the formula for inductive reactance.
An inductor resists alternating current through its reactance:
\[ X_L = \omega L = 2\pi f L \] This plays the role of resistance for AC circuits, but causes no energy dissipation.

Step 2: Calculate the angular frequency.
$f = 50\,\text{Hz}$:
\[ \omega = 2\pi \times 50 = 100\pi\,\text{rad/s} \]

Step 3: Compute the inductive reactance.
$L = 70\,\text{mH} = 70 \times 10^{-3}\,\text{H}$:
\[ X_L = 100\pi \times 70 \times 10^{-3} = 7\pi\,\Omega \]

Step 4: Simplify using the approximation $\pi \approx 22/7$.
\[ X_L = 7 \times \frac{22}{7} = 22\,\Omega \]

Step 5: Apply Ohm's law for AC to find rms current.
For a purely inductive circuit:
\[ I_\text{rms} = \frac{V_\text{rms}}{X_L} = \frac{220}{22} = 10\,\text{A} \]

Step 6: State the answer.
\[ \boxed{10\,\text{A}} \]