Assertion: If an inductor coil is connected to DC source, the current supplied by it is `I_(1)`. If the same coil is connected with an AC source of same voltage. Then current is `I_(2)`, then `I_(2) lt I_(1)`.
Reason: In AC circuit, inductor coil offers more resistance.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the given problem, we need to analyze the assertion and reason provided in the question step by step.

### Step 1: Understand the Assertion
The assertion states that when an inductor coil is connected to a DC source, the current supplied is \( I_1 \). When the same coil is connected to an AC source of the same voltage, the current is \( I_2 \), and it claims that \( I_2 < I_1 \).

### Step 2: Analyze the Behavior of the Inductor in DC
When an inductor is connected to a DC source, it behaves like a short circuit after a transient period. The current through the inductor can be calculated using Ohm's law:
\[ I_1 = \frac{V}{R} \]
where \( V \) is the voltage of the DC source and \( R \) is the resistance of the circuit.

### Step 3: Analyze the Behavior of the Inductor in AC
When the same inductor is connected to an AC source, the inductor introduces inductive reactance (\( X_L \)), which affects the total impedance (\( Z \)) of the circuit. The impedance in an AC circuit with an inductor is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]
The current in the AC circuit can be calculated as:
\[ I_2 = \frac{V}{Z} \]

### Step 4: Compare the Currents
Since \( Z \) (impedance) is always greater than \( R \) (resistance) in an AC circuit with an inductor, we can conclude:
\[ I_2 = \frac{V}{Z} < \frac{V}{R} = I_1 \]
Thus, \( I_2 < I_1 \) is indeed correct.

### Step 5: Understand the Reason
The reason states that in an AC circuit, the inductor coil offers more resistance. This is true because the inductive reactance \( X_L \) contributes to the total impedance \( Z \), making it larger than just the resistance \( R \). Therefore, the current \( I_2 \) is reduced due to the increased total impedance.

### Conclusion
Both the assertion and the reason are correct, and the reason correctly explains the assertion.

### Final Answer
Both assertion and reason are correct, and the reason is the correct explanation for the assertion.

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