Question

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

Answer 1

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

Voltage across the $\text{AC}$ source is, $V_{rms}=\sqrt{(V{}_R{)}^2+(V_C-V_L{)}^2}$

Substituting the data given in the question,

$V_{rms}=\sqrt{{\left(40\right)}^2+{(80-40)}^2}=\sqrt{{40}^2+{40}^2}=40\sqrt{2}\text{V}$.