Question

In an $AC$ circuit shown, if the emf of the source at an instant is $5\text{V}$, the potential difference across the capacitor at the same instant is $4\text{V}$. The potential difference across $R$ at that instant may be

• A. $3\text{V}$
• B. $9\text{V}$
• C. $\frac{3}{\sqrt{2}}\text{V}$
• D. None of these

Answer 1

The correct option is D None of these

Given:-

At any instant

$V_{\text{source}}=5\text{V}$

$V_{\text{capacitor}}=4\text{V}$

Using <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Kirchhoff's Voltage Law for the loop at any instant, we can write

$V_{\text{source}}=V_{\text{resistor}}+V_{\text{capacitor}}$

Here $V_{\text{source}},V_{\text{Resistor}}\text{and}{V}_{\text{Capacitor}}$ are the instantaneous Potential differences

So, $5=V_{\text{Resistor}}+4$

$\Rightarrow V_{\text{Resistor}}=1\text{V}$

Hence, option $\left(D\right)$ is correct.