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  4. 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 ?

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Q. 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 $R$ ?

Current Electricity

Solution:

Let resistors $P, Q$, and $R$ have resistance $r$. The effective resistance across the source is
$R_{ eff }=r+r \| r=r+\frac{(r)(r)}{r+r}=r+\frac{r}{2}=\frac{3 r}{2}$
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
$I^{2} r=\left(\frac{2}{r}\right) r=2\, W$