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In the circuit of the preceding example (Fig.) the potentiometer has a scale 50 cm long graduated in millimetres; the galvanometer sensitivity is 10-4 A per division: the internal resistance of the accumulator is 0.5Ω. What should be the resistance of the galvanometer to detect the imbalance when the potentiometer arm is moved by one scale division from the balance position?

 

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Answer: 39.5 ohms.

Explanation:

When the potentiometer arm is moved from the position of balance, the current in the galvanometer is determined by the difference between the e.m.f. of the accumulator and the potential drop across points A and B due to the standard cell. When the potentiometer arm is moved by one division, the 'difference in potential increases or falls by the value

where n is the number of divisions on the potentiometer scale. If X is the resistance of the galvanometer, the current through it may be found from the equation.

of X is that which would produce, for a movement of the potentiometer arm by one division, a current of 10-4A, which is sufficient to deflect the galvanometer pointer by one division, i.e.

 

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