MHT CET · Physics · Experimental Physics

Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at $40 cm$ from left end. A $30 Ω$ resistance is connected in series with the smaller of the two resistances, the null point shifts by $20 cm$ to the right end. The value of smaller resistance in $Ω$ is

A $12$
B $24$
C $36$
D $48$

Verified Solution

Answer & Solution

Correct Answer

(B) $24$

Step-by-step Solution

Detailed explanation

l_{x} = 40 cm, l_{R} = 60 cm

\frac{x}{R} = \frac{l_{x}}{l_{R}} = \frac{40}{60} = \frac{2}{3}

....... (i)

∴ \frac{x + 30}{R} = \frac{60}{40} = \frac{3}{2}

∴ \frac{x + 30}{R} = \frac{3}{2}

∴ 2x (+ 30) = 3 R

R = \frac{2 (x + 30)}{3}

........ (ii)
From (i) and (ii),

\frac{3 x}{2 (x + 30)} = \frac{2}{3}

9 x = 4 x + 120

5 x = 120 \Rightarrow x = 24 Ω

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at 40 cm from left end. A 30 Ω resistance is connected in series with the smaller of the two resistances, the null point shifts by 20 cm to the right end. The value of smaller resistance in Ω is

Step-by-step Solution