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°.

Let us analyze the given series LCR circuit step-by-step to find the current and the phase angle between the current and the voltage.

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

2. Calculate the total impedance (Z) of the series circuit:
In a series LCR circuit, the impedance $Z$ is given by the formula:
$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$

Substituting the given values:
$Z=\sqrt{{20}^2+{\left(45-25\right)}^2}$
$Z=\sqrt{{20}^2+{20}^2}$
$Z=\sqrt{400+400}$
$Z=\sqrt{800}=20\sqrt{2}\text{Ω}$

Using the approximation $\sqrt{2}\approx 1.414$:
$Z\approx 20\times 1.414=28.28\text{Ω}$

3. Calculate the RMS current (I) in the circuit:
The current is determined using Ohm's law for AC circuits:
$I=\frac{V_{\mathrm{rms}}}{Z}$
$I=\frac{220}{20\sqrt{2}}=\frac{11}{\sqrt{2}}$
$I\approx \frac{11}{1.414}\approx 7.78\text{A}\approx 7.8\text{A}$

4. Calculate the phase angle (φ) between the current and the voltage:
The phase angle $\phi$ is given by:
$\tan \left(\phi \right)=\frac{X_L-X_C}{R}$

Substituting the values:
$\tan \left(\phi \right)=\frac{45-25}{20}=\frac{20}{20}=1$

Since $\tan (\phi )\; =\; 1$, the phase angle is:
$\phi ={\tan }^{-1}\left(1\right)=45°$

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