Question

In case of meter bridge experiment balance length for $2\Omega$ and $3\Omega$ is $\ell$ and for $x\Omega$ and $3\Omega$ is $(\ell + 10)$ cm. Find $x$.

Hint:

Always substitute the balance length correctly while applying the meter bridge ratio formula.

Answer 1

Correct Answer: 30

Step 1: Use proportionality of resistance and balance length

In a meter bridge at balance condition, resistance is directly proportional to the balancing length of the wire.

R ∝ ℓ

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Step 2: Compare the first balance condition

When resistances 2 Ω and 3 Ω are connected, the balance length is ℓ.

So,

2 / 3 = ℓ / (100 − ℓ)

Solving,

ℓ = 40 cm

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Step 3: Use change in balance length information

When resistance 2 Ω is replaced by x Ω, the balance point shifts by 10 cm.

New balance length = 40 + 10 = 50 cm

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Step 4: Apply proportionality for the new arrangement

Now the ratio of resistances equals the ratio of balance lengths:

x / 3 = 50 / 50

x / 3 = 1

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Step 5: Final calculation

x = 30 Ω

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Final Answer:

The value of the unknown resistance is
x = 30 Ω