Alternating voltage E=200sin 300t is applied across series combination of R=10ohms and an inductor of 800mH .calulate the impedance and power factor of the circuit?

The impedance of the circuit can be calculated using the formula:

Z = √(R^2 + (ωL)^2)

Where:
R = 10 ohms
ω = 300 (angular frequency)
L = 800mH = 0.8H

Z = √(10^2 + (300*0.8)^2)
Z = √(100 + 57600)
Z = √57700
Z ≈ 240.1 ohms

The power factor of the circuit can be calculated using the formula:

cosφ = R/Z

cosφ = 10/240.1
cosφ ≈ 0.0416

Therefore, the impedance of the circuit is approximately 240.1 ohms and the power factor is approximately 0.0416.

Impedance (Z):

```
Z = sqrt(R^2 + XL^2)
```

where:
- R = Resistance = 10 ohms
- XL = Inductive reactance = 2πfL = 2π - 300 Hz - 800 mH = 480 ohms

```
Z = sqrt(10^2 + 480^2) = 480.07 ohms
```

Power Factor (cos φ):

```
cos φ = R / Z
```

```
cos φ = 10 / 480.07 = 0.021
```

Therefore, the impedance of the circuit is 480.07 ohms and the power factor is 0.021.