Question

A $\text{LCR}$ series combination is connected to an $AC$ source. If voltage across the inductor, capacitor, resistor are $40\text{V},80\text{V}$ and $40\text{V}$ respectively. Then the source voltage of the $AC$ source is

• A. $40\sqrt{2}\text{V}$
• B. $80\text{V}$
• C. $80\sqrt{2}\text{V}$
• D. $100\sqrt{2}\text{V}$

Answer 1

The correct option is A $40\sqrt{2}\text{V}$

$V_R=40\text{V};V_C=80\text{V};V_L=40\text{V}$

We know that, $V_{rms}=\sqrt{{\left(V{}_R\right)}^2+[V_C-V_L{]}^2}$

Substituting the data given in the question,

$V_{rms}=\sqrt{{40}^2+[80-40{]}^2}=\sqrt{{40}^2+{40}^2}=40\sqrt{2}\text{V}$.

Hence, option (a) is the correct answer.