A 2.2 k Ω resistor and a 2.0 μF capacitor are connected in series in an ac circuit. The rms voltages across each are equal. What is the frequency?
A) 23 Hz
B) 15 Hz
C) 72 Hz
D) 36 Hz
E) There is insufficient information to solve.

Question

Quizplus · Accepted Answer

We know that the voltage across the resistor and capacitor are equal. Let's call this voltage V.

The impedance of a capacitor is given by:

Zc = 1/(2πfC)
where f is the frequency and C is the capacitance.

The impedance of a resistor is simply the resistance itself, R.

In a series circuit, the total impedance is given by:

Z = √(R^2 + Zc^2)

Since the voltages across each element are equal, we know that the current is the same throughout the circuit. By Ohm's law, we can relate the voltage to the current and impedance:

V = IZ

Combining these equations, we get:

V = IR + IZc

Substituting for Zc and solving for f, we get:

f = 1/(2πRC)

Plugging in the given values, we get:

f = 1/(2π(2.2kΩ)(2.0μF))

f ≈ 36 Hz

Therefore, the answer is D.

A 22 K Ω Resistor and a 2