Transformers — Question 1

Question 1

An ideal step-down transformer trades voltage for current at unchanged power

An ideal transformer has 600 primary turns and 150 secondary turns. Its primary receives 120 V rms and its secondary drives a 12.0-ohm resistor. Ignore magnetizing current.

1. Find secondary voltage, secondary current, and primary current.

2. Find input power, output power, and resistance seen at the primary.

Question 1 - Solution

An ideal step-down transformer trades voltage for current at unchanged power

(a) Method and calculation

$$V_s/V_p=N_s/N_p=1/4\Rightarrow V_s=30.0\,V,\quad I_s=V_s/R_L=2.50\,A.$$$$\boxed{I_p=(N_s/N_p)I_s=.625\,A}.$$

(b) Interpretation and further calculation

$$P_s=V_sI_s=75.0\,W=V_pI_p=P_p.$$$$\boxed{R_{\mathrm{in}}=(N_p/N_s)^2R_L=192\,\Omega}.$$

Physical check

The current ratio is inverse to the voltage ratio; an ideal transformer cannot amplify real power.