A 400-Ω resistor and a capacitor are connected in parallel across a 300-Hz source.If the amplitude of the current in the resistor is equal to that in the capacitor,what is the value of the capacitance? A) 1.33 × 10^-6 F B) 0.750 × 10^-6 F C) 10.6 × 10^-6 F D) 0.212 F

Question

Quizplus · Accepted Answer

Using the formula for the impedance of a capacitor in parallel with a resistor:

Z = R || (1/jωC)

Where R is the resistance, C is the capacitance, ω is the angular frequency (2πf), and || means parallel.

Since the resistor and capacitor have equal currents, we can equate the amplitudes of their impedances:

|Z_R| = |Z_C|
|r| = |1/jωC|
|r| = ωC

Substituting the given values:

400 = 2π(300)C

Solving for C:

C = 1.33 × 10^-6 F, which is choice A.

A 400-Ω Resistor and a Capacitor Are Connected in Parallel