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  • .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 <img alt="" src

.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

Option: 1

2 W


Option: 2

6 W


Option: 3

3 W


Option: 4

8 W


Answers (1)

best_answer

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

\mathrm{R_{\text {eff }}=r+r \| r=r+\frac{(r)(r)}{r+r}=r+\frac{r}{2}=\frac{3 r}{2} }

Current drawn from source is

\begin{aligned} &\mathrm{ I_S^2 R_{\text {eff }}=12 }\\ &\mathrm{ \Rightarrow I_2=\sqrt{\frac{12}{R_{\text {eff }}}=\sqrt{\frac{8}{r}} \mathrm{~A}}} \\ \end{aligned}
Since Q and R have equal resistance r, each draws a current of I which is given by \mathrm{I=\frac{1}{2} I_S=\sqrt{\frac{2}{r}} \mathrm{~A}}

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

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

Posted by

Shailly goel

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