Question

In an LCR circuit, voltages across the components are $V_L$, $V_C$, $V_R$ respectively when connected to a AC source $V=V_{0}sin\left(\omega t\right)$. The relation between $V$, $V_R$, $V_C$ and $V_L$ is.

• A. $V=V_R+V_L+V_C$
  
• B. $V=[V_R^2+V_L^2+V_C^2{]}^{1/2}$
• C. $V=[V_R^2+(V_L-V_C{)}^2{]}^{1/2}$
• D. $V=[V_R^2+(V_L+V_C{)}^2{]}^{1/2}$

Answer 1

The correct option is C $V=[V_R^2+(V_L-V_C{)}^2{]}^{1/2}$

Voltages $V_R,V_L$ & $V_C$ are perpendicular to each other, as shown in the diagram-

$V_R$ is along current $I$,

$V_L$ leads current by ${90}^o$ white

$V_C$ lags current by ${90}^o$.

$\Rightarrow$ Reactive voltage $\left(V_X\right)$ is $=V_L-V_C$

Using Pythagoras theorem,

$V^2=V_R^2+(V_L-V_C{)}^2$

$\Rightarrow V=[V_R^2+(V_L^2-V_C^2){]}^{1/2}$