Question

If we change the value of $R$, then

• A. Voltage does not change on $C$
• B. Voltage does not change on $L$
• C. Voltage change on $LC$ combination
• D. Voltage does not change on $LC$ combination

Answer 1

The correct option is C

Voltage change on $LC$ combination

1. We know that the current in a series $LCR$ circuit impressed by an ac emf $V=V_0\cos \omega t$ is given by
2. $i=I_0\cos \left(\omega t-\varphi \right)$,
3. where $I_0=\frac{V_0}{\sqrt{R^2+{\left(\omega L-{\displaystyle \frac{1}{\omega C}}\right)}^2}}$ and $\varphi ={\tan }^{-1}\frac{\omega L-{\displaystyle \frac{1}{\omega C}}}{R}$
4. The RMS voltage is $V_r=I_r\left(\sqrt{R^2+{\left(\omega L-\frac{1}{\omega C}\right)}^2}\right)$, $\left(1\right)$
5. where $V_r$ is the RMS voltage. Thus, $I_r$ depends on the frequency $\omega$ of the impressed ac emf, $R$ is the resistance, $C$ is the capacitance and $L$ is the inductance.
6. Hence, if we change the value of $R$, then voltage changes on the combination.

Hence, option C is correct.