Question

An inductor of 50.0 mH is connected to a source of 220 V. Then the rms current in the circuit will be ……. . The frequency of the source is 50 Hz.  

Hint:

The inductive reactance of an inductor is given by \( X_L = 2\pi f L \). The RMS current in an AC circuit with only an inductor is given by \( I_{{rms}} = \frac{V_{{rms}}}{X_L} \).

Answer 1

Step 1: Understanding Inductive Reactance 
In an AC circuit, an inductor offers inductive reactance (\(X_L\)), which is given by: \[ X_L = 2\pi f L \] where:
- \( X_L \) is the inductive reactance (in ohms),
- \( f \) is the frequency of the AC source (in Hz),
- \( L \) is the inductance (in Henry). 
Step 2: Given Values 
- \( L = 50.0 \) mH = \( 50.0 \times 10^{-3} \) H,
- \( f = 50 \) Hz,
- \( V_{{rms}} = 220 \) V. 
Step 3: Calculating Inductive Reactance 
\[ X_L = 2\pi \times 50 \times (50.0 \times 10^{-3}) \] \[ X_L = 2\pi \times 2.5 \] \[ X_L = 5\pi \approx 15.7 \, \Omega \] 
Step 4: Calculating RMS Current 
The RMS current (\( I_{{rms}} \)) is given by: \[ I_{{rms}} = \frac{V_{{rms}}}{X_L} \] \[ I_{{rms}} = \frac{220}{15.7} \] \[ I_{{rms}} \approx 14 { A} \] Thus, the rms current in the circuit is \( 14 \) A.