If the power dissipated in the 3,Omega resist | vedclass

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(A) $1$. First,calculate the equivalent resistance of the parallel combination of $2\,\Omega$ and $4\,\Omega$ resistors:$R_p = \frac{2 	imes 4}{2 + 4

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$8$

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(A) $1$. First,calculate the equivalent resistance of the parallel combination of $2\,\Omega$ and $4\,\Omega$ resistors:$R_p = \frac{2 	imes 4}{2 + 4} = \frac{8}{6} = \frac{4}{3}\,\Omega$.$2$. The circuit consists of a $3\,\Omega$ resistor in series with the parallel combination $(4/3\,\Omega)$.$3$. Since the same current $I$ flows through the $3\,\Omega$ resistor and the parallel combination,the power $P = I^2 R$ is proportional to resistance $(P \propto R)$.$4$. Let $P_p$ be the power in the parallel combination: $\frac{P_{3\Omega}}{P_p} = \frac{3}{4/3} \Rightarrow \frac{27}{P_p} = \frac{9}{4} \Rightarrow P_p = 12\,W$.$5$. The voltage across the parallel combination is $V_p = \sqrt{P_p 	imes R_p} = \sqrt{12 	imes \frac{4}{3}} = \sqrt{16} = 4\,V$.$6$. The power dissipated in the $2\,\Omega$ resistor is $P_2 = \frac{V_p^2}{2} = \frac{4^2}{2} = \frac{16}{2} = 8\,W$.

If the power dissipated in the $3\,\Omega$ resistor is $27\,W$,what is the power dissipated in the $2\,\Omega$ resistor (in $,W$)?

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