Question

An $LCR$ series $AC$ circuit is at resonance with $10\, V$ each across $L, C$ and $R$. If the resistance is halved, the respective voltages across $L, C$ and $R$ are

• A. $10\, V, 10 \,V$ and $5\, V$
• B. $10\, V, 10\, V$ and $10\, V$
• C. $20\,V, 20\,V$ and $5\,V$
• D. $20\, V$, $20\, V$ and $10\, V$
• E. $5\, V$, $5 \,V$ and $5\, V$

Answer 1

Answer: (D)

When resistance is halved current will be doubled
$ V_{R}^{}=2i\times \frac{R}{2}=10\,V $
$ V_{L}^{}=2i\times {{X}_{L}}=2\times 10=20\,V $
$ V_{C}^{}=2i\times {{X}_{C}}=2\times 10=20\,V $