Current Electricity

JEE Main level, numerical answer, medium

147 of 380

Question 147 of 380

The series combination of two batteries, both of the same emf 10V,10V, but different internal resistance of 20Ω20 \Omega and 5Ω,5 \Omega , is connected to the parallel combination of two resistors 30Ω30 \Omega and xΩ.\text{x}\Omega . The voltage difference across the battery of internal resistance 20Ω20 \Omega is zero, the value of x\text{x} (in Ω)\Omega ) is____

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Answer: 30

V1=ϵ1−i.r1{V}_{1}={ϵ}_{1}-i.{r}_{1}
0=10−i×200=10-i\times 20
i=0.5Ai=0.5A
V2=7.530+7.5x{V}_{2}=\dfrac{7.5}{30}+\dfrac{7.5}{\text{x}}
0.5=0.25+7.5x0.5=0.25+\dfrac{7.5}{\text{x}}
7.5x=0.25x=7.50.25=30Ω\dfrac{7.5}{\text{x}}=0.25 \text{x}=\dfrac{7.5}{0.25}=30\Omega

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