Question

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:

Options

• 7.8 A and 30°

• 7.8 A and 45°

• 15.6 A and 30°

• 15.6 A and 45°

Answer 1

7.8 A and 45°

Explanation:

Given: R = 20 Ω

X_C = 25 Ω

X_L = 45 Ω

V = 220 V (rms)

Formula: `Z = sqrt(R^2 + (X_L - X_C)^2)`

= `sqrt(20^2 + (45 - 25)^2)`

= `sqrt(20^2 + 20^2)`

= `sqrt(400 + 400)`

= `20sqrt2  Ω`

I = `V/Z`

= `220/(20sqrt2)`

= `11/sqrt2`

= 7.8 A

tan Φ = `(X_L - X_C)/R`

⇒ tan Φ = `(45 - 25)/20`

⇒ tan Φ = `20/20` 

⇒ tan Φ = 1

⇒ Φ = tan⁻¹(1)

∴ Φ = 45°