The following circuit shows the use of potentiometer to measure the internal resistance of a cell:
When the key is open, how does the balance point change, if the current from the driver cell decreases?
When the key K is closed, how does the balance point change if R is increased keeping current from the driver cell constant?
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When current through driver cell decreases, the potential gradient across potentiometer wire decreases; so the balancing length $\text{l}=\frac{\text{E}}{\text{k}}$ increases, so balance point is shifted to the right.
With increase of R, the terminal p.d. across cell E increases and hence balancing length $\text{l}=\frac{\text{V}}{\text{k}}\propto\text{V}$ increases. So the balance point is shifted to the right.
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