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Question -

Obtain the answers to (a) and (b)in Exercise 7.15 if the circuit is connected to a 110 V, 12 kHz supply? Hence,explain the statement that a capacitor is a conductor at very high frequencies.Compare this behaviour with that of a capacitor in a dc circuit after thesteady state.



Answer -

Capacitance of thecapacitor,┬аC┬а= 100 ╬╝F = 100 ├Ч 10тИТ6┬аF

Resistance of the resistor,┬аR┬а=40 ╬й

Supply voltage,┬аV┬а=110 V

Frequency of the supply,┬а╬╜┬а=12 kHz = 12 ├Ч 103┬аHz

Angular Frequency,┬а╧Й┬а=2 ╧А╬╜= 2 ├Ч ╧А ├Ч 12 ├Ч 10303

= 24╧А ├Ч 103┬аrad/s

Peakvoltage,┬а
Maximum current,┬а

For an┬аRC┬аcircuit,the voltage lags behind the current by a phase angle of┬а╬ж┬аgivenas:

Hence,┬а╬ж┬аtendsto become zero at high frequencies. At a high frequency, capacitor C acts as aconductor.

In a dc circuit, after the steadystate is achieved,┬а╧Й┬а= 0. Hence, capacitor C amounts to anopen circuit.

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