Q101 / 180 · NEET 2025 · Physics

To an ac power supply of 220 V at 50 Hz , a resistor of $20 \Omega$, a capacitor of reactance $25 \Omega$ and an inductor of reactance $45 \Omega$ are connected is series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively-

  • A
    7.8 A and $30^{\circ}$
  • Correct answer
    B
    7. 8 A and $45^{\circ}$
  • C
    15.6 and $30^{\circ}$
  • D
    15.6 and $45^{\circ}$

Solution

$\begin{aligned} & \mathrm{X}_{\mathrm{C}}=25 \Omega \\ & \mathrm{X}_{\mathrm{L}}=45 \Omega \\ & \mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2} \\ & \mathrm{Z}=\sqrt{20^2+(45-25)^2} \\ & \mathrm{Z}=20 \sqrt{2}\end{aligned}$ $\begin{aligned} & I_{r m s}=\frac{V_{r m s}}{Z}=\frac{220}{20 \sqrt{2}}=\frac{11}{\sqrt{2}}=7.8 \mathrm{~A} \\ & \tan \phi=\frac{X_L-X_C}{R}=\frac{45-25}{20}=\frac{20}{20}=1 \\ & \phi=45^{\circ}\end{aligned}$

Hence, the correct answer is option: 'B'.

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