JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Current Electricity

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Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance x cm from A. The galvanometer shows zero deflection.

The value of x, to nearest integer, is ____

Answer: 48

Solution

The

12 Ω

and

6 Ω

resistors form one pair of arms, the two parts AP and PB of the wire form the other, and the galvanometer bridges C and P. Zero deflection is the balance condition of this Wheatstone bridge,

\frac{12}{6} = \frac{R _{A P}}{R _{P B}}

The wire is uniform, so its resistance is proportional to its length and

\frac{x}{72 - x} = 2

. This gives

3 x = 144

, so

x = 48

cm.

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Integer answer

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