Transformers — Question 2

Question 2

A transformer can match a resistive load to a source resistance

An AC source has 12.0 V rms open-circuit voltage and series resistance 50.0 ohms. It drives an 8.00-ohm load through an ideal transformer. Let $a=N_p/N_s$.

1. Choose a for maximum real load power.

2. Find that power and secondary rms voltage and current.

Question 2 - Solution

A transformer can match a resistive load to a source resistance

(a) Method and calculation

$$R_{\mathrm{reflected}}=a^2R_L,\quad P_L=\frac{V_{\mathrm{oc}}^2a^2R_L}{(R_s+a^2R_L)^2}.$$$$\boxed{a=\sqrt{R_s/R_L}=2.50}.$$

(b) Interpretation and further calculation

$$P_{L,\max}=V_{\mathrm{oc}}^2/(4R_s)=144/200=.720\,W.$$$$\boxed{V_s=V_{\mathrm{oc}}/(2a)=2.40\,V,\quad I_s=V_s/R_L=.300\,A}.$$

Physical check

Maximum transfer here dissipates equal power in source resistance and load; it is not maximum efficiency.