Question

A $1000\,\Omega$ resistance and a capacitor of $100\,\Omega$ resistance are connected in series to a $220\,V$ source. When the capacitor is $50\%$ charged, the value of the displacement current is:
(A) $11.\sqrt 2 \,A$
(B) $2.2\,A$
(C) $11\,A$
(D) $4.4\,A$

Answer 1

Hint
The value of the displacement current is determined by using the displacement current formula, by using the voltage and the resistance value which are given in the question, the value of the displacement of the current can be determined.
The displacement of the current is given by,
$\Rightarrow {I_D} = \dfrac{{{V_0}}}{{{X_C}}}$
Where, ${I_D}$ is the displacement current, ${V_0}$ is the voltage in the circuit and ${X_C}$ is the resistance of the capacitor.

Complete step by step answer
Given that, The total resistance of the system is, $R = 1000\,\Omega$
The resistance of the capacitor is, ${X_C} = 100\,\Omega$
The total voltage of the system is, ${V_0} = 220\,V$
Then the source of the capacitor is $50\%$ charged, the half of the capacitor is charged.
Now, The displacement of the current is given by,
$\Rightarrow {I_D} = \dfrac{{{V_0}}}{{{X_C}}}\,......................\left( 1 \right)$
By substituting the total voltage in the circuit and the resistance of the capacitor in the above equation (1), then the equation (1) is written as,
$\Rightarrow {I_D} = \dfrac{{220\,V}}{{100\,\Omega }}$
By dividing the terms in the above equation, then the above equation is written as,
$\Rightarrow {I_D} = 2.2\,A$
Thus, the above equation shows the displacement current for the given information.
Hence, the option (B) is the correct answer.

Note
The displacement of the current is directly proportional to the voltage in the circuit and inversely proportional to the resistance of the capacitor. As the voltage in the circuit increases, the displacement current in the circuit also increases. As the voltage in the circuit decreases, the displacement current in the circuit also decreases. If the resistance in the circuit increases, the displacement current decreases. If the resistance in the circuit decreases, the displacement current increases.