Question

A parallel plate capacitor made of circular plates each of radius $R=6.0\text{cm}$ has a capacitance $C=100\text{pF}$. The capacitor is connected to a $230\text{V}$ AC supply with an angular frequency of $300\text{rad/s}$. The displacement current is -

• A. $7.2\mu \text{A}$
• B. $7.8\mu \text{A}$
• C. $6.9\mu \text{A}$
• D. $6.1\mu \text{A}$

Answer 1

The correct option is C $6.9\mu \text{A}$

We know that, $i_d=i=i_{\text{rms}}$

Now, capacitive reactance,

$X_C=\frac{1}{\omega C}=\frac{1}{300\times 100\times {10}^{-12}}=\frac{{10}^8}{3}\Omega$

So,

$i_d=i_{\text{rms}}=\frac{V_{\text{rms}}}{X_C}=\frac{230}{\frac{{10}^8}{3}}=6.9\times {10}^{-6}\text{A}=6.9\mu \text{A}$

Hence, option $\left(C\right)$ is the correct answer.