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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?

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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

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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