A 2.0-μF capacitor in series with a 2.0-kΩ resistor is connected to a 60-Hz ac source. Calculate the impedance of the circuit.
A) 1 500 ohms
B) 1 800 ohms
C) 2 100 ohms
D) 2 400 ohms
E) 8 600 ohms

Question

Quizplus · Accepted Answer

The impedance of the circuit can be calculated using the formula Z = √(R² + Xc²), where R is the resistance and Xc is the reactance of the capacitor.

Since the capacitor has a capacitance of 2.0 μF and is connected to a 60-Hz ac source, the capacitive reactance can be calculated using the formula Xc = 1/(2πfC), where f is the frequency and C is the capacitance.

Xc = 1/(2π(60)(2.0×10^-6)) 
Xc = 1326.2 ohms

The resistance is given as 2.0 kΩ.

Z = √(R² + Xc²) 
Z = √((2.0×10³)² + (1326.2)²) 
Z = 2400 ohms

Therefore, the impedance of the circuit is 2 400 ohms, which is option D.

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