Question

A parallel plate capacitor (fig.) made of circular plates each of radius $R=6.0cm$ has a capacitance $C=100\mu F$. The capacitor is connected to a $230V$ ac supply with a (angular) frequency of $300$ rad $s^{-1}$. What is the $rms$ value of the conduction current?

Answer 1

Given: A parallel plate capacitor made of circular plates each of radius R=6.0 cm has a capacitance $C=100\mu F$. The capacitor is connected to a 230 V ac supply with a (angular) frequency of $300rad{s}^{-1}.$

To find the rms value of the conduction current

Solution:

Radius of plates, $R=6cm=6\times {10}^{-2}m$

Capacitance of capacitor, $C=100\mu F=100\times {10}^{-6}F={10}^{-4}F$

Voltage of capacitor, $V=230V$

Frequency of capacitance, $\omega =300rad/s$

The rms value of the current

$I_{rms}=\frac{V_{rms}}{X_C}...........\left(i\right)$

And $X_C=\frac{1}{\omega C}$

Substituting this in eqn(i), we get

$I_{rms}=\frac{V_{rms}}{\frac{1}{\omega C}}⟹I_{rms}=Vrms\times \omega \times C⟹I_{rms}=230\times 300\times {10}^{-4}⟹I_{rms}=69\times {10}^3\times {10}^{-4}=6.9A$

is the rms value of the conduction current