Question

The $rms$ value of conduction current will be:
(A) $5.7\mu A$
(B) $6.3\,\mu A$
(C) $9.6\,\mu A$
(D) $6.9\,\mu A$

Answer 1

The $rms$ is the root means square value and it is the direct current which would create the same average power dissipation in a resistive load. Use th4 formula of the $rms$ value of the current and substitute the calculated value of the capacitive reactance in it to find the value of the $rms$ of the conduction current.

Useful formula:
(1) The formula of the $rms$ value of the current is given by
$I = \dfrac{V}{{{X_c}}}$
Where $I$ is the $rms$ value of the current, $V$ is the potential difference and ${X_c}$ is the capacitive reactance.
(2) The capacitance reactance is given by
${X_c} = \dfrac{1}{{\omega C}}$
Where $\omega$ is the angular frequency and $C$ is the capacitance.

Complete step by step solution:
In order to find the $rms$ value of the alternating current, take the formula of the $rms$ of the current
$I = \dfrac{V}{{{X_c}}}$
Substitute the formula of the capacitive reactance in the above step,
$I = \dfrac{V}{{\dfrac{1}{{\omega C}}}}$
By simplifying the above step, we get
$I = V \times \omega C$
Substitute the value of the potential difference, angular frequency and the capacitance in the above step.
$I = 230 \times 300 \times 100 \times {10^{ - 12}}$
By simplifying the above step,
$I = 6.9 \times {10^{ - 6}}\,A$
Substituting the $\mu m = {10^{ - 6}}\,m$ in the above step,
$I = 6.9\,\mu A$

Thus the option (D) is correct.

Note: The root means the square value of the sinusoidal wave is calculated by multiplying the $14.14$ with the value of the peak voltage of the sinusoidal wave. The average value of the alternating current cannot be found, since it is obtained as zero. Hence the $rms$ value is used to compare both alternating and the direct current and also the effective value of the alternating current.