A series alternating current (AC) circuit consists of a resistor of resistance 6\ \Omega a… — JAMB UTME

A series alternating current (AC) circuit consists of a resistor of resistance $6\ \Omega$ and an inductor with inductive reactance $8\ \Omega$ . What is the total impedance of the circuit?

$10\ \Omega$ Answer
B
$14\ \Omega$
C
$2\ \Omega$
D
$48\ \Omega$

Answer

The total impedance of the circuit is

10\ \Omega

In a series RL alternating current circuit, total impedance

Z

combines resistance

R

and inductive reactance

X_L

as perpendicular vector components. Using

Z = \sqrt{R^2 + X_L^2}

, substituting

R = 6\ \Omega

and

X_L = 8\ \Omega

gives

Z = \sqrt{6^2 + 8^2} = \sqrt{100} = 10\ \Omega

Step-by-Step Solution

Identify the given values for resistance and inductive reactance.

R = 6\ \Omega

and

X_L = 8\ \Omega

These are the resistive and reactive opposition components in the series RL circuit.

Apply the impedance formula for a series RL circuit.

Z = \sqrt{R^2 + X_L^2}

Voltage across a resistor and an inductor are

90^\circ

out of phase, requiring vector/phasor addition to determine total impedance.

Calculate the magnitude of total impedance.

Z = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10\ \Omega

Evaluating the square root yields the net opposing effect to AC current flow.

Key Concept

Impedance in a Series RL Circuit

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic