Question

An electrical engineer is working with a parallel AC circuit. The circuit draws 8 ohms on a resistive branch, and the angle of the total impedance is 35°. What is the approximate number of ohms on the inductive branch?
A.0.7
B.4.59
C.5.6
D.6.55

Answer 1

Answer:

C) 5.6

Step-by-step explanation:

In an AC circuit, the current changes periodically direction, following a sine-like function.

As a result, we have the following:

- The current through the resistive branch of the circuit is always in phase with the voltage

- However, the voltage in the inductive branch of the circuit preceeds the current by a phase difference of 90 degrees

The inductance of the circuit therefore is basically the resultant vector of the resistance (R) and the inductance (L), and the phase angle is related to the two quantities by the relationship:

$tan \theta = \frac{L}{R}$

In this problem, we have:

$\theta=35^{\circ}$ is the phase angle

$R=8 \Omega$ is the resistance of the circuit

Therefore, the inductance is:

$L=R tan \theta = (8)(tan 35^{\circ})=5.6 \Omega$