The potentiometer wire AB shown in figure is 50 cm long. When AD = 30 cm, no deflection occurs in the galvanometer. Find R.

Concepts/Formula used:
Wheatstone bridge:

The condition for no deflection through the galvanometer is
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Here
and
.
When no deflection occurs, ![]()
Let the resistance per cm of the potentiometer wire be be ρ .
Hence,
and
.
Using the equation when there is no deflection for a Wheatstone bridge/potentiometer, we have
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