An inductor coil is connected to a 12V battery and drawing a current 24 A. This coil is connected to capacitor and an AC source of rms voltage rating 24 V in the series connection. The rms current through the circuit would found to be

Options

A. 48 A
B. 36 A
C. 0
D. 24 A

Explanation

To solve the problem step by step, we will follow the reasoning and calculations as outlined in the video transcript.

### Step 1: Identify the given parameters
- Voltage across the inductor coil (V1) = 12 V
- Current through the inductor coil (I1) = 24 A
- RMS voltage of the AC source (VRMS) = 24 V

### Step 2: Calculate the inductive reactance (XL)
The inductive reactance (XL) can be calculated using the formula:
\[ XL = \frac{V1}{I1} \]
Substituting the known values:
\[ XL = \frac{12 \, \text{V}}{24 \, \text{A}} = 0.5 \, \Omega \]

### Step 3: Calculate the total RMS current (IRMS)
The total RMS current in the circuit can be calculated using the formula:
\[ IRMS = \frac{VRMS}{R} \]
Where R is the total resistance in the circuit. In this case, since we only have the inductive reactance (XL) and no resistive component is mentioned, we will assume that the inductor's reactance is the only opposition to the current.

Substituting the values:
\[ IRMS = \frac{VRMS}{XL} = \frac{24 \, \text{V}}{0.5 \, \Omega} = 48 \, \text{A} \]

### Conclusion
The RMS current through the circuit is:
\[ IRMS = 48 \, \text{A} \]