Question

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

• A. $2W$
• B. $6W$
• C. $3W$
• D. $8W$

Answer 1

Answer: (A)

Let resistors $P,Q$, and $R$ have resistance $r$. The effective resistance across the source is
$R_{eff}=r+r\Vert r=r+\frac{(r)(r)}{r+r}=r+\frac{r}{2}=\frac{3r}{2}$
Current drawn from source is
$I_s^2{R}_{\text{eff }}=12$
or $I_s=\sqrt{\frac{12}{R_{\text{eff }}}}=\sqrt{\frac{8}{r}}A$
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
$I^{2}r=\left(\frac{2}{r}\right)r=2W$