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  4. In the circuit shown in figure, power developed across 1 Ω, 2 Ω and 3 Ω resistances are in the ratio.

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Q. In the circuit shown in figure, power developed across $1\, \Omega, 2\, \Omega$ and $3\, \Omega$ resistances are in the ratio.Physics Question Image

AP EAMCETAP EAMCET 2018

Solution:

Current distribution is as shown in figure
image
$\therefore $ Powers are
$P_{1}=I_{1}^{2} R_{1}=\frac{4}{9} i^{2},$
$P_{2}=I_{2}^{2} R_{2}=\frac{2}{9} i^{2}$,
and $P_{3}=I_{3}^{2} R_{3}=3 i^{2}$
$=\frac{27}{9} i^{2}$
$\Rightarrow \, P_{1}: P_{2}: P_{3}:: 4: 2: 27$