You are given a sealed box with two electrical terminals. The box contains a 5.0

Question

You are given a sealed box with two electrical terminals. The box contains a 5.00 ohm resistor in series with either an inductor or a capacitor. When you attach an ac generator with an rms voltage of 0.750 V to the terminals of the box, you find that the current increases with increasing frequency. a) Does the box contain an inductor or a capacitor? Explain b) When the frequency of the generator is 25.0 kHz, the rms current is 87.2 mA. What is the capacitance or inductance of the unknown component in the box?

Ans. capacitor, .910mF

Explanation / Answer

Here ,

as the current increases with increasing frequency

Z must decrease with increase in frequency ,

for Capacitor , X = 1/(2pi * f * C)

hence , there must be a capacitor in the box.

b)

Vrms = 0.750 V

Irms = 87.2 mA

as Vrms/Irms = Z

0.750/.0872 = sqrt(R^2 + (1/(2pi * f * C))^2)

0.750/.0872 = sqrt(5^2 + (1/(2pi * 25 *10^3 * C))^2)

solving for C

C = 9.097 *10^-7 F = .910 uF

the capcitance is .910 uF

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