Question

In an $AC$ circuit, the voltage is given by $V=110sin2\pi \left(60\right)t$.The voltage across the inductor, capacitor as well as resistor:

• A. must be less than 110 $V$
• B. must be less than 220 $V$
• C. may be more or less than 110 $V$
• D. may be more than 110 $V$ across $L$ or $C$ but must be less than 110 $V$ across $R$.

Answer 1

Answer: (D)

may be more than 110 $V$ across $L$ or $C$ but must be less than 110 $V$ across $R$.

RMS value of voltage source

$V_s$ = 110 volts

$V_s=\sqrt{{V_R}^2+{\left(V_L-V_C\right)}^2}$
where $V_R$,$V_L$, $V_C$ is voltage across resistance, inductor and capacitor.
From above formula it's obvious that $V_R$ or $(V_L-V_C)$ can't be larger than $V_s.$
So, difference of $V_L$ & $V_L$ should less than $V_s\left(110V\right).$
But individual value of $V_L$ and $V_C$ may be grater than 110 volts.
So, D is correct answer.