Obtain an expression for the potential gradient ‘k’ of potentiometer whose wire of length l has a resistance r. The driving cells has an emf E, is connected in series with an external resistance R.

Solution

Given,
Length of the potentiometer wire = l
Internal resistance of the wire = r
Emf of the driving cell =E
External resistance of the cell = R

Current drawn by the wire, I= $\frac{E}{R + r}$

Now, using Ohm's law V =IR

i.e, V = $\frac{ER}{R + r}$

Now, potential gradient of the wire is given by
k = V/l
= $\frac{ER}{(R + r) l}$

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Current Electricity

Obtain an expression for the potential gradient ‘k’ of potentiometer whose wire of length l has a resistance r. The driving cells has an emf E, is connected in series with an external resistance R.

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