Question

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 emt `ε/2` and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in the figure shows no deflection is ______.

 

Options

• `5/12` L

• `11/12` L

• `13/24` L

• `11/24` L

Answer 1

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 emt `ε/2` and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in the figure shows no deflection is `underlinebb(13/24 "L")`.

Explanation:

Given, the length of the wire, AB = L

Resistance of wire, AB = 12r

emf of cell D = ε, internal resistance of D = r

emf of cell C = `ε/2`, internal resistance of C = 3r

Current in potentiometer wire (i) = `"Total emf"/"Total resistance"`

`i = ε/(r + 12r) = ε/(13r)`

The potential drop across the balance length AJ of the potentiometer wire is V_AJ = i × R_AJ

⇒ V_AJ = i(resistance per unit length × length AJ)

V_AJ = `i((12r)/L xx x)`

where x is the balance length AJ.

As a null point  occurs at J, so potential drop across balance length,

AJ = emf of cell C

V_AJ = `ε/2 ⇒ i((12r)/L xx x) = ε/2`

⇒ `ε/(13r) xx (12r)/L xx x = ε/2 ⇒ x = 13/24` L