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Question

A 6 V battery with negligible internal resistance is connected across a uniform wire of length 100 cm. The positive terminal of another battery of emf 4 V and internal resistance 1 Ω is connected at A as shown in the figure. Take the potential at B to be zero and find out which of the following is correct?

A
The potential at A is 6 V and at C is 2 V.
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B
The potential is 4 V on AB at a distance of 66.67 cm from A.
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C
If C is connected at 66.67 cm from A, then there will be no current in the 4 V battery.
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D
If the 6 V battery is replaced by a 12 V battery, then the potential at A would be 8 V.
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Solution

The correct option is C If C is connected at 66.67 cm from A, then there will be no current in the 4 V battery.Given, VB=0 As AB is connected to battery of 6 V VA−VB=6 V VA=6 V As C is open, VA−VC=4 VC=4 V Potential gradient K=Vl=6100=0.06 V/cm When C is connected to AB such that AC=x cm As no current flows, VAC=4 V=xK x=40.06=66.67cm If the 6 V battery is replaced by a 12 V battery, then VA−VB=12 V⇒VA=12 V

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