In an experiment with a potentiometer, V_B = 10V. R is adjusted to be 50Ω (Fig. 3.9). A student wanting to measure voltage E₁ of a battery (approx. 8V) finds no null point possible. He then diminishes R to 10Ω and is able to locate the null point on the last (4^th) segment of the potentiometer. Find the resistance of the potentiometer wire and potential drop per unit length across the wire in the second case.

Question

Philoid · Accepted Answer

Consider R^’ to be the resistance of the potentiometer wire.

When R=50Ω, no null point is found,

Effective value of resistance = R^’ + 50Ω

I =

IR^’ = < 8V

10R^’V < 400VΩ + 8R^’V

R^’ < 200Ω

Similarly, when R=10Ω, null point is found,

Hence,

Also,

Now, In the second case,

Potential drop across 400cm > 8V

Potential drop across 300cm < 8V

Let k be potential drop per unit length

And,

Hence resistance of the potentiometer wire lies between 160Ω and 200Ω and the potential drop per unit length lies between 8/3Vm^-1 and 2Vm^-1.