The capacitor in the figure below is designed to filter low-frequency signals, i

Question

The capacitor in the figure below is designed to filter low-frequency signals, impeding their transmission between circuits.

(a) What capacitance is needed to produce a 136 k reactance at a frequency of 230 Hz?


(b) What would its reactance be at 1.00 MHz?


(c) What are the implications of your answers to (a) and (b)? (Select all that apply.)

The capacitor does what it is designed to do.

Reactance is smaller at high frequencies.

Reactance is larger at high frequencies.

High frequencies transmit better than low ones.

The capacitor does not do what it is designed to do.

Low frequencies transmit better than high ones.

Explanation / Answer

a)

Xc = 1 / 2pi*fC

C = 1 / 2pi*f*Xc

C = 1 / (2pi x 230 x 136 x 10^3)

C = 5.088 x 10^-9 F = 5.088 nF

b)

Xc = 1 / 2pi*f*C

Xc = 1 / (2pi x 1 x 10^6 x 5.088 x 10^-9)

Xc = 31.28 ohms

c)

The reactance from the capacitor at high frequencies is much smaller than that at lower frequencies, so the

capacitor does indeed allow the high frequencies to short to ground much better than the low frequencies, therefore

working as it is designed to.

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