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

The correct option is 7.8 A and 45°.

To find the current in the series LCR circuit and the phase angle between the current and the voltage, we can follow these step-by-step calculations:

1. Identify the given values:
RMS Voltage of the AC supply, $V=220\text{V}$
Frequency of the AC supply, $f=50\text{Hz}$
Resistance, $R=20\Omega$
Capacitive reactance, $X_C=25\Omega$
Inductive reactance, $X_L=45\Omega$

2. Calculate the total impedance ($Z$) of the circuit:
The impedance in a series LCR circuit is given by the formula:

$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$

Substitute the given values into the equation:

$Z=\sqrt{{20}^2+{\left(45-25\right)}^2}$

$Z=\sqrt{{20}^2+{20}^2}$

$Z=\sqrt{400+400}=\sqrt{800}=20\sqrt{2}\Omega$

Since $\sqrt{2}\approx 1.414$:

$Z\approx 20\times 1.414=28.28\Omega$

3. Calculate the current ($I$) in the circuit:
Using Ohm's law for AC circuits, the current is:

$I=\frac{V}{Z}$

$I=\frac{220}{20\sqrt{2}}=\frac{11}{\sqrt{2}}$

$I\approx \frac{11}{1.414}\approx 7.78\text{A}\approx 7.8\text{A}$

4. Calculate the phase angle ($\varphi$) between current and voltage:
The tangent of the phase angle is given by:

$tan\varphi =\frac{X_L-X_C}{R}$

Substitute the reactance and resistance values:

$tan\varphi =\frac{45-25}{20}=\frac{20}{20}=1$

Since $tan\varphi =1$, the phase angle is:

$\varphi ={45}^{\circ }$

Thus, the current in the circuit is approximately 7.8 A and the phase angle is 45°.