Question

An ac voltage V = 280 sin(100π t) volt is connected across a series LCR circuit in which R = 400 Ω, L = `5/π` H and C = `50/π` µF. Taking `sqrt(2) = 1.4`, calculate: 

1. Impedance of the circuit.
2. Rms value of current that flows in the circuit.
3. Power factor of the circuit.

Answer 1

Given: V = 280 sin(100π t)

V₀ = 280 V

ω = 100π

(I) Inductive Reactance (X_L) = ωL

= `100 pi xx 5/pi`

= 500 Ω

Capacitive reactance `(X_C) = 1/(ωC)`

= `1/(100pi xx (50/pi xx 10^-6)`

= `10^6/5000`

= 200 Ω

Net reactance (X) = X_L − X_C

= 500 − 200

= 300 Ω

Impedance (Z) = `sqrt(R^2 + X^2)`

= `sqrt(400^2 + 300^2)` 

= `sqrt(160000 + 90000)` 

= `sqrt(250000)` 

= 500 Ω

(II) `V_(rms) = (V_0)/sqrt2`

= `280/1.4`

= 200 V
`I_(rms) = (V_(rms))/Z`

= `200/500`

= 0.4 A

(III) cos ϕ = `R/Z`

= `400/500`

= 0.8