Question

A $100\Omega$ resistance and a capacitor of $100\Omega$ reactance are connected in series across a $220V$ source. When the capacitor is $50percent$ charged, then what will be the peak value of the displacement current?

A.2.2A

B.1.41A

C.4.4A

D.$11\sqrt{2}A$

Answer 1

The value of the impedance of the circuit can be found by taking the square root of the sum of the square of resistance and the square of the reactance. The peak value of displacement current will be the ratio of the maximum voltage of the source to the impedance of the circuit. This will help you in answering this question.

Complete answer:

It has been mentioned in the question that the resistance of the resistor connected in the circuit can be written as,

$R=100\Omega$

The reactance of the capacitor which is connected in this circuit can be mentioned as,

$X=100\Omega$

The maximum voltage of the source connected will be given as,

$V=220V$

The value of the impedance of the circuit can be found by taking the square root of the sum of the square of resistance and the square of the reactance. This can be shown as an equation as,

$Z=\sqrt{{{R}^{2}}+{{X}^{2}}}$

Substituting the values in it will give,

$Z=\sqrt{{{100}^{2}}+{{100}^{2}}}=100\sqrt{2}\Omega$

At the condition where the capacitor which is $50percent$ charged, the maximum voltage can be written as,

${{V}_{\max }}=\dfrac{110}{\sqrt{2}}V$

Therefore the peak value of displacement current will be the ratio of the maximum voltage of the source to the impedance of the circuit. That is we can write that,

$I=\dfrac{{{V}_{\max }}}{Z}=\dfrac{110\sqrt{2}}{100\sqrt{2}}=2.2A$

Hence the peak value of the displacement current has been obtained.

The answer has been given as option A.

Note: Impedance is defined as the measure of the total opposition provided by a circuit to current. In another way, we can say that it is the amount at which the circuit impedes the flow of charge. It is similar to resistance, but it also considers the effects of capacitance and inductance. Impedance can be expressed in ohms.