The total length of potentiometer wire AB is 50 cm in the arrangement as shown in figure. If P is the point where the galvanometer shows zero reading then the length AP is ____ cm.

potentiometer works on the principle of wheatstone bridge.

 Length of segment AP = $$x$$
 Length of segment PB = $$50 - x$$

resistance of potentiometer wire directly prorportional to length($$R = \rho \frac{l}{A}$$)

The balancing condition for the Wheatstone bridge is:

$$ \frac{R_1}{R_2} = \frac{\text{Length of AP}}{\text{Length of PB}} $$
$$ \frac{R_1}{R_2} = \frac{x}{50 - x} $$

$$ \frac{6}{4} = \frac{x}{50 - x} $$

$$x$$=30cm