Question

The adjoining figure shows an $AC$ circuit with resistance $R$, inductance $L$ and source voltage $V_S$. Then,

• A. The source voltage $V_S=72.8\text{V}$.
• B. The phase angle between current and source voltage is ${\tan }^{-1}\left(\frac{7}{2}\right)$.
• C. Both $\left(A\right)$ and $\left(B\right)$ are correct.
• D. Both $\left(A\right)$ and $\left(B\right)$ are wrong.

Answer 1

The correct option is A The source voltage $V_S=72.8\text{V}$.

The current through $R$ and $L$ will be the same. The Phasor diagram of the circuit is shown below.


From phasor diagram

$V_S^2=V_R^2+V_L^2={70}^2+{20}^2=5300$

$\Rightarrow V_S=\sqrt{5300}\approx 72.8\text{V}$

And the phase difference between the current and voltage is given by,

$\tan \varphi =\frac{V_L}{V_R}=\frac{20}{70}$

$\Rightarrow \varphi ={\tan }^{-1}\left(\frac{2}{7}\right)$

Hence, option $\left(A\right)$ is correct.