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

Question

In the circuit shown in figure, power developed across 1 Ω, 2 Ω and 3 Ω resistances are in the ratio. (A) 1: 2: 3 (B) 4: 2: 27 (C) 6: 4: 9 (D) 2: 1: 27

Tardigrade Admin · Accepted Answer

Current distribution is as shown in figure

∴

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

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

1 : 2 : 3

4 : 2 : 27

6 : 4 : 9

2 : 1 : 27

Current distribution is as shown in figure

$∴$ 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 $P_{3} = I_{3}^{2} R_{3} = 3 i^{2}$
$= \frac{27}{9} i^{2}$
$\Rightarrow P_{1} : P_{2} : P_{3} :: 4 : 2 : 27$

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