When an inductor L and a resistor R are connected across 12 V, 50 Hz a.c. supply, a current of 0.5 A flows through the distance the circuit. What is the value of R if current differs in phase from applied voltage by `pi//3` radian?

Explanation

To solve the problem, we need to find the value of the resistor \( R \) in an RL circuit where the current lags the voltage by \( \frac{\pi}{3} \) radians. Here are the steps to find the value of \( R \):

### Step 1: Understand the relationship between voltage, current, and impedance in an RL circuit.
In an RL circuit, the total impedance \( Z \) is given by:
\[ Z = \sqrt{R^2 + (X_L)^2} \]
where \( X_L \) is the inductive reactance given by:
...