Question

Resistors P, Q, and R in the circuit have equal resistances. If the battery is supplying a total power of 12 W, what is the power dissipated as heat in resistor R?

• A. 2 W
• B. 6 W
• C. 3 W
• D. 8 W

Answer 1

The correct option is A 2 W

Let resistors P, Q, and R have resistance r. The effective resistance across the source is

$R_{eff}=r+r||r=r+\frac{\left(r\right)\left(r\right)}{r+r}=r+\frac{r}{2}=\frac{3r}{2}$

Current drawn from source is

$I_s^2{R}_{eff}=12$ or $I_s=\sqrt{\frac{12}{R_{eff}}}=\sqrt{\frac{8}{r}}A$

Since Q and R have equal resistance r, each draws a current of I, which is given by

$I=\frac{1}{2}{I}_s=\sqrt{\frac{2}{r}}A$

Heat dissipation in R can now be determined and is given by

$I^{2}r=\left(\frac{2}{r}\right)r=2W$