Question

I have a circuit established like this: http://i.stack.imgur.com/tsmjJ.png

The question is to calculate the maximum voltage the battery is allowed to provide, so each resistor can achieve their maximum power.

My attempt: I tried using P=V^2/R and find out the max voltage for battery is 100V, but then I used P=I^2R to verify the circuit, it doesn't work.

I've tried for 4 hours and can't find why.

Does anyone have an idea? Thank you so much!

Answer 1

The current required to dissipate 25W in the resistor that is not in parallel is found from
\[P=I ^{2}R\]
\[25=I ^{2} \times 100\]
\[I=\sqrt{\frac{25}{100}}=\frac{1}{2}\ amp\]
This maximum allowed current of 0.5A will divide between the paralleled resistors giving 0.25 A through each of them. Therefore the power dissipated in each of the paralleled 100 ohm resistors will be
\[(0.25)^{2} \times 100=6.25W\]
Therefore there is no way that the circuit can achieve the target of the three resistors running at 25W each.