A student in a lab took a coil and connected it to a `12 VDC` source. He measures the steady state current in the circuit to be `4 A`. He then replaced the `12 VDC` source by a `12V,(omega=50rad//s)AC` source and observes that the reading in the `AC` ammeter is `2.4 A`. He then decides to connect a `2500 muF` capacitor in series with the coil and calculate the average power developed in the circuit. Further he also decides to study the variation in current in the circuit (with the capacitor and the battery in series).
The value of resistance of the coil calculated by the student is

Options

A. `3Omega`
B. `4Omega`
C. `5Omega`
D. `8Omega`

Explanation

To solve the problem, we need to find the resistance of the coil based on the information provided. Here’s the step-by-step solution:

### Step 1: Understand the DC Circuit
The student initially connected a coil to a `12 V DC` source and measured a steady-state current of `4 A`.

### Step 2: Calculate the Resistance in the DC Circuit
Using Ohm's Law, we can calculate the resistance (R) of the coil in the DC circuit. Ohm's Law states:
\[ R = \frac{V}{I} \]
Where:
- \( V \) is the voltage (12 V)
- \( I \) is the current (4 A)

Substituting the values:
\[ R = \frac{12 \, \text{V}}{4 \, \text{A}} = 3 \, \Omega \]

### Step 3: Conclusion
The resistance of the coil calculated by the student is \( 3 \, \Omega \).

### Final Answer
The value of resistance of the coil calculated by the student is **3 ohms**.

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