Q123 / 160 · JIPMER 2010 · Physics
In a series $L-C-R$ circuit, resistance $R=10 \Omega$ and the impedance $Z=10 \Omega$. The phase difference between the current and the voltage is
- Correct answerA$0^{\circ}$
- B$30^{\circ}$
- C$45^{\circ}$
- D$60^{\circ}$
Solution
Impedance,
$\begin{aligned}
Z & =\sqrt{R^2+\left(X_L-X_C\right)^2} \\
\therefore \quad 10 & =\sqrt{(10)^2+\left(X_L-X_C\right)^2} \\
\Rightarrow \quad 100 & =100+\left(X_L-X_C\right)^2 \\
\Rightarrow X_L-X_C & =0....(i)
\end{aligned}$
Let $\phi$ is the phase difference between current and voltage
$\begin{aligned}
\therefore & & \tan \phi & =\frac{X_L-X_C}{R} \\
\therefore & & \tan \phi & =\frac{0}{R} \\
& \Rightarrow & \phi & =0
\end{aligned}$
[from Eq. (i)]
Hence, the correct answer is option: 'A'.