Question

A series $L-C-R$ circuit is connected to a source of alternating emf of $50V$ and the potential difference across inductor and capacitor is $90V$ and $60V$, respectively. The potential difference across the resistor is

• A. $70V$
• B. $60V$
• C. $40V$
• D. $80V$

Answer 1

Answer: (C)

Given, $V=50V,V_L=90V,V_C=60V$
In $L-C-R$ circuit,
$\therefore V=\sqrt{V_R^2+{\left(V_L-V_C\right)}^2}$
$\Rightarrow V^2=V_R^2+{\left(V_L-V_C\right)}^2$
$50^2=V_R^2+(90-60{)}^2$
$\Rightarrow 2500=V_R^2+900$
$\Rightarrow V_R^2=1600$
$\Rightarrow V_R=\sqrt{1600}=40V$