Question

An input potential V_in = 200 sin 100 πt V is provided to an ideal transformer having 1000 turns in the primary coil and 100 turns in the secondary coil as shown in the figure. The load circuit has a resistance of 4Ω, a capacitive reactance of 2Ω, and an inductive reactance of 6Ω.

Find:

1. the output voltage across the load circuit.
2. the current is flowing through the load circuit.
3. the power supplied to the load circuit by the transformer.

Answer 1

Given:

Input voltage, V_in = 200 sin 100 πt V

Primary turns, N_p = 1000

Secondary turns, N_s = 100

Load: R = 4 Ω, X_c = 2 Ω,  X_L = 6 Ω

i. Output voltage across load circuit:

`V_s= N_s/N_p V_p`

= `100/1000 xx 200 sin 100 πt V`

= 0.1 × 200 sin 100 πt V

= 20 sin 100 πt V

ii. Current flowing through load circuit:

Net reactance:

X = X_L − X_C

= 6 − 2

= 4 Ω

Impedance:

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

= `sqrt(4^2 + 4^2)`

= `sqrt(16 + 16)`

= `sqrt32`

= 5.66 Ω

RMS voltage of secondary:

Secondary output, V_s = 20 sin 100 πt

Peak value, V_m = 20 V

`V_"rms" = V_m/sqrt2`

= `20/sqrt2`

= 14.14 V

Current through the load:

I = `V_"rms"/Z`

= `14.14/5.66`

= 2.5 A

iii. Power supplied to the load:

Power factor:

`cos phi = R/Z`

= `4/5.66`

= 0.707

Real power:

P = V_rms ​I cos ϕ

= 14.14 × 2.5 × 0.707

= 25 W