In the following circuit, 5Ωresistor develops 45 J/sdue to current flowing through it. The  power developed across 12Ω resistor is

# In the following circuit, $5\Omega$resistor develops due to current flowing through it. The  power developed across $12\Omega$ resistor is

1. A

16 W

2. B

192 W

3. C

36 W

4. D

64 W

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### Solution:

${R}_{eff}=12+\frac{15×5}{20}$$=\frac{63}{4}$

$V=i×\frac{63}{4}$

$i=\frac{4V}{63}$

$i={i}_{1}+{i}_{2}$

$15{i}_{2}=5{i}_{1}$

${i}_{1}=3{i}_{2}⇒{i}_{2}=\frac{{i}_{1}}{3}$

$i={i}_{1}+\frac{{i}_{1}}{3}=\frac{4{i}_{1}}{3}$

$P={i}_{1}^{2}×5$

$45={i}_{1}^{2}×5⇒{i}_{1}^{2}=9$

${i}_{1}=3$

power developed through

Resistor is $=P={i}^{2}×R$

$={4}^{2}×12$

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