A standerd cell emf `1.08 V `is balance by the potential difference across `91 cm` of a meter long wire applied by a cell of emf `2 V` through a series resistor of resistance `2 Omega`. The internal resistance of the cell is zero. Find the resistance per unit length of the potentiometer wire.

Explanation

First consider the lower branch separately, You have to find the total potential drop V across the potentiometer wire of resistance r using unitary method . If 91 cm balances 1.08 volt them 1 m balances `(1.08)/(91) xx 100 = 1.18" l volt"`
Now using eqn . (ii) `V_(s) - V = IR ` gives `2 - 1.18 = l xx 2`
` therefore l = 0.41 A`
Then using equation (ii) V = Ir , we have `r = (V)/(l) = (1.18)/(0.41) = 2.87 Omega`
`therefore ` Resistance per unit lenght is `2.87 Omega//m` .