In an experiment on metre bridge, if the balancing length AC is 'x' . What would be its value, when the radius of the metre bridge wire AB is doubled? Justjfy the answer.

Consider the figure below.

here AC =x and the resistance of segments AC and BC are R_{AC} and R_{BC }respectively.

Now, the condition of no deflection dictates that

R/r = R_{AC}/R_{BC}

If the resistance of AB is doubled, the ratio R/r or R_{AC}/R_{BC} will remain unchanged.

Thus, the balancing length AC= x will stay the same.

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