AC Circuit Question?

Question

A step-up transformer is designed to have an output voltage of 2200 V (rms) when the primary is connected across a 110 V (rms) source.

(a) If the primary winding has 76 turns, how many turns are required on the secondary?

___ turns

(b) If a load resistor across the secondary draws a current of 1.30 A, what is the current in the primary, assuming ideal conditions?

___A

(c) If the transformer actually has an efficiency of 88.0%, what is the current in the primary when the secondary current is 1.20 A?

___A

Answer 1

(a) Transformation ratio → α = V_1/V_2 = N_1/N_2

α = V_1/V_2 = 110V/2200V = 0.05 → step-up transformer

N_2 = N_1 * V_2/V_1 = 76 t * 2200V/110V = 1520 turns

(b) α = V_1/V_2 = N_1/N_2 = (ideally) I_2/I_1

I_1 = I_2/α = 1.30A/0.05 = 26.0A

(c) Real transformer so transformation ratio does not apply.  We must put more power into transformer to make up for losses.

Output = S_2 = V_2 * I_2 = 2200V * 1.2A = 2.64 kV•A

Efficiency = Output/Input * 100% = S_2/S_1 * 100%

S_1 = S_2 * 100%/Efficiency = 2.64 kV•A/0.88 = 3.00kV•A

I_1 = S_1/V_1 = 3.00kV•A/110V = 27.3A