Transformer Turns Ratio and Current Calculation

This problem requires calculating the secondary current ($I_s$) of an ideal transformer using its apparent power rating (VA), primary voltage ($V_p$), and the turns ratio ($N_p:N_s$).

Given Information

• Apparent Power Rating (VA): P = 220 VA
• Primary Voltage: $V_p$ = 220 V
• Turns Ratio: $N_p : N_s$ = 4:1
• Transformer type: Ideal

Steps to Calculate Secondary Current

1. Calculate Secondary Voltage ($V_s$): The voltage ratio in an ideal transformer equals the turns ratio: $ \frac{V_p}{V_s} = \frac{N_p}{N_s} $ Substitute the known values: $ \frac{220 \text{ V}}{V_s} = \frac{4}{1} $ Solve for $V_s$: $ V_s = \frac{220 \text{ V} \times 1}{4} = 55 \text{ V} $

2. Calculate Secondary Current ($I_s$): In an ideal transformer, apparent power is conserved ($P_p = P_s = 220$ VA). Apparent power is the product of voltage and current ($P = V \times I$). Use the secondary voltage ($V_s$) and secondary apparent power ($P_s$) to find the secondary current ($I_s$): $ P_s = V_s \times I_s $ Substitute the values: $ 220 \text{ VA} = 55 \text{ V} \times I_s $ Solve for $I_s$: $ I_s = \frac{220 \text{ VA}}{55 \text{ V}} = 4 \text{ A} $

Result

The secondary current ($I_s$) for this ideal transformer is 4 A.