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Question

A battery having emf E1=100 V and internal resistance r=0.5 Ω is connected to a storage battery of emf E2=90 V and external resistance R as shown in figure. For what value of R no current will pass through storage battery E2?


A
5.5 Ω
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B
4.5 Ω
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C
2.5 Ω
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D
7.5 Ω
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Solution

The correct option is B 4.5 Ω
Let that no current passes through battery E2, therefore the current supplied by power supply E1 will flow through resistance R in a closed circuit.


For the loop ABCDA,

i=E1R+r

i=100R+0.5 .........(1)

Now potential at points E and F can be related by KVL,

VEiR=VF

VEVF=iR

Also the potential difference across E and F will same as emf of battery E2.

E2=iR

i=E2R=90R .....(2)

From Eq.(1) and (2),

90R=100R+0.5

90R+45=100R

R=4.5 Ω

Hence, option (b) is correct.
Why this question ?It intends to test your understanding offlow of current in a closed loop & Ohm'slaw across a component element/resistance.

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