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Question

# A 5V battery with internal resistance 2Ω and a 2V battery with internal resistance 1Ω are connected to a 10Ω resistor as shown in figure, the current in 10Ω resistor is?

A
0.27A
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B
0.31A
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C
0.031A
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D
0.53A
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Solution

## The correct option is C 0.031AStep 1: Assuming Batteries to be in Parallel [Refer Figure 1]The given circuit can be redrawn as in Figure 1.We can assume both batteries to be in parallel connected to 10Ω resistance.In parallel battery combination:Eeqreq=E1r1+E2r2 ....(1)Where, 1req=1r1+1r2 =12+11=32 ⇒ req=23ΩHere the polarities are unlike, So E1=5V and E2=−2VSo, Equation (1) ⇒ Eeq2/3=52−21=0.5⇒ Eeq=13Step 1: Solving Equivalent circuit [Refer Figure 2]Req=req+10Ω=323ΩHence, Applying KVL on equivalent circuit, we get:i=EeqReq=132=0.031 AOption C is the correct answerAlternate Solution:∙ Assume currents in all three branches.∙ Aply KCL at any one junction (Either P1 or P2) to find relation between the currents. ∙ Apply KVL in both left and right loops, and obtain the current in 10Ω resistance.

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