A potentiometer wire AB having length L and resistance 12r is...

A potentiometer wire

AB

having length

L

and resistance

12r

is joined to a cell

D

of emf

ε

and internal resistance

r

. A cell

C

having EMF

ε / 2

and internal resistance

3r

is connected. The length

AJ

, at which the galvanometer, as shown in the figure, shows no deflection is

A potentiometer wire AB having length L and resistance 12r is joined to a cell D of emf ε and internal resistance r . A

A potentiometer wire AB having length L and resistance 12r is joined to a cell D of emf ε and internal resistance r . A

Options

A $\dfrac{5}{12}L$
B $\dfrac{11}{24}L$
C $\dfrac{11}{12}L$
D $\dfrac{13}{24}L$

Correct answer

D. $\dfrac{13}{24}L$

Step-by-step solution

Potential difference across

AJ = I{R}_{AJ}

= \dfrac{ε}{13r} \cdot \left(\dfrac{12r}{L} \cdot x\right)

For no current in galvanometer,

\dfrac{ε}{2} =

potential difference across

AJ

\dfrac{ε}{2} = \dfrac{12ε}{13L}x

x = \dfrac{13L}{24}

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