In a metre bridge experiment the balance point is obtained if the gaps are closed by $2\,\Omega$ and $3\,\Omega$. A shunt of $X\,\Omega$ is added to $3\,\Omega$ resistor to shift the balancing point by 22.5 cm. The value of X is ______

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Current Electricity

In a metre bridge experiment the balance point is obtained if the gaps are closed by

2 Ω

and

3 Ω

. A shunt of

X Ω

is added to

3 Ω

resistor to shift the balancing point by 22.5 cm. The value of X is ______

Answer: 2

In the metre bridge the balancing length from the

2 Ω

end satisfies

\frac{2}{3} = \frac{ℓ}{100 - ℓ}

, which gives

ℓ = 40

cm. Placing the shunt

X

in parallel with the

3 Ω

arm lowers that arm to

\frac{3 X}{3 + X}

, so the balance length grows by

22.5

cm to

62.5

cm. The new balance condition is

\frac{2}{\frac{3 X}{3 + X}} = \frac{62.5}{37.5} = \frac{5}{3}

, so

6 (3 + X) = 15 X

, giving

18 = 9 X

. The shunt resistance needed is

2 Ω

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Integer answer