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:
[tex]tan \theta = \frac{L}{R}[/tex]
In this problem, we have:
[tex]\theta=35^{\circ}[/tex] is the phase angle
[tex]R=8 \Omega[/tex] is the resistance of the circuit
Therefore, the inductance is:
[tex]L=R tan \theta = (8)(tan 35^{\circ})=5.6 \Omega[/tex]
