What capacitance is needed in series with a 30 $\Omega$ resistor at 1.0 kHz for a total impedance of 45 $\Omega$ ?
A) 34$\mu$F
B) 15 $\mu$F
C) 4.7 $\mu$F
D) 0.037 $\mu$F

Question

Quizplus · Accepted Answer

We can use the formula for total impedance of a series circuit containing a capacitor and a resistor:

Z = sqrt(R^2 + (1/(2πfC))^2)

where Z is the total impedance, R is the resistance, f is the frequency, and C is the capacitance.

Plugging in the values given:

45 Ω = sqrt((30 Ω)^2 + (1/(2π(1000 Hz)C))^2)

Solving for C:

C = 4.7 μF

Therefore, the answer is choice C, 4.7 μF.

What Capacitance Is Needed in Series with a 30 Ω\OmegaΩ Resistor at 1

What Capacitance Is Needed in Series with a 30 $\Omega$ Resistor at 1