JEE Main 2026 — Jan 21, Shift 2 — Physics solution

JEE Main2026Jan 21, Shift 2Physics

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.

A
15
B
30
C
25
D
20

Solution

At null deflection, the potential drop across the 6 $Ω$ resistor matches the drop across length AP of the wire, while the drop across 4 $Ω$ matches PB.

So $\frac{6}{R _{A P}} = \frac{4}{R _{P B}}$ , which (since wire resistance is proportional to length) gives $\frac{ℓ _{A P}}{ℓ _{P B}} = \frac{6}{4} = \frac{3}{2}$ .

With $ℓ_{A P} + ℓ_{P B} = 50$ cm, we get $ℓ_{A P} = \frac{3}{5} \times 50 = 30$ cm.

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