Chapter 12, Problem 1TFQ

In an ac circuit where $R=X_L,$ the phase angle is ${45}^{°}.$

To determine

To find: Whether in an ac circuit for the given condition is $45°$ or not.

Explanation of Solution

Given:

For an ac circuit, where $R=X_L$ .

The phase angle is $45°$ .

Calculation:

Drawing the general ac circuit diagram for the series RL circuit:

  

From the above diagram, the total impedance of the circuit is given as:

  $Z=R+j{X}_L$

The phase angle for the circuit is given as:

  $\begin{array}{l}\text{Since,}\\ R=X_L\\ \text{Therefore,}\\ \varphi ={\text{tan}}^{-1}\frac{X_L}{R}\\ \varphi ={\text{tan}}^{-1}1\\ \varphi =\text{45}°\end{array}$

Hence, the given result is correct.