A battery having emf E1=100V and internal resistance r=0.5Ω is connected to a storage battery of emf E2=90V and external resistance R as shown in figure. For what value of R no current will pass through storage battery E2?
A
5.5Ω
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B
4.5Ω
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C
2.5Ω
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D
7.5Ω
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Solution
The correct option is B4.5Ω 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,
VE−iR=VF
VE−VF=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=4.5Ω
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.