Question 3.7: Find the current and power supplied by the 40 V source in th...

We are interested only in the current and power drain on the 40 V source, so the problem has been solved once we obtain the equivalent resistance across the terminals of the source. We can find this equivalent resistance easily after replacing either the upper Δ (100, 125, 25 Ω)  or the lower Δ (40, 25, 37.5 Ω) with its equivalent Y. We choose to replace the upper Δ We then compute the three Y resistances, defined in Fig. 3.33, from  Eqs. 3.44to 3.46

R_{1}=\frac{R_{b}R_{c}}{R_{a}+R_{b}+R_{c}} ,

R_{2}=\frac{R_{c}R_{a}}{R_{a}+R_{b}+R_{c}} ,

R_{3}=\frac{R_{a}R_{b}}{R_{a}+R_{b}+R_{c}} .

Thus,

R_{1}=\frac{100\times 125}{250}=50\Omega ,

R_{2}=\frac{125\times 25}{250}=12.5\Omega ,

R_{3}=\frac{100\times 25}{250}=10\Omega .

Substituting the Y-resistors into the circuit shown in Fig. 3.32 produces the circuit shown in Fig. 3.34. From Fig. 3.34, we can easily calculate the resistance across the terminals of the 40 V source by series-parallel simplifications:

R_{eq}=55+ \frac{\left(50\right)\left(50\right) }{100}=80\Omega .

The final step is to note that the circuit reduces to an 80Ω resistor across a 40 V source, as shown in Fig. 3.35, from which it is apparent that the 40 V source delivers 0.5 A and 20 W to the circuit.