College

A series circuit is connected to a 50 V, 60 Hz source. It is made up of a 25-ohm resistor, a capacitor with \( X_C = 18 \) ohms, and an inductor with \( X_L = 24 \) ohms. What is the circuit impedance?

A. \( 25.7 \, \Omega \)
B. \( 29.2 \, \Omega \)
C. \( 32.4 \, \Omega \)
D. \( 35.9 \, \Omega \)

Answer :

Answer:

the impedance of the circuit is 25.7 ohms.

Explanation:

It is given that,

Voltage, V = 50 volts

Frequency, f = 60 Hz

Resistance, R = 25 ohms

Capacitive resistance, [tex]X_C=18\ ohms[/tex]

Inductive resistance, [tex]X_L=24\ ohms[/tex]

We need to find the impedance of the circuit. It is given by :

[tex]Z=\sqrt{R^2+(X_L-X_C)^2}[/tex]

[tex]Z=\sqrt{25^2+(24-18)^2}[/tex]

Z = 25.7 ohms

So, the impedance of the circuit is 25.7 ohms. Hence, this is the required solution.

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