MHT CET · Physics · Experimental Physics

With a resistance of ‘X’ in the left gap and a resistance of 9 $Ω$ in the right gap of meter bridge, the balance point is obtained at 40 cm from the left end. In what way and to which resistance $3 Ω$ resistance be connected to obtained the balance at 50 cm from the left end?

A In series with $9 Ω$
B Parallel to $X Ω$
C In series with $X Ω$
D Parallel to $9 Ω$

Verified Solution

Answer & Solution

Correct Answer

(C) In series with $X Ω$

Step-by-step Solution

Detailed explanation

The balance condition of bridge is shown below in the first case

Then,

\frac{X}{9} = \frac{40}{60} \Rightarrow X = \frac{2}{3} \times 9 = 6 Ω

To get the balance point at 50 cm from left end, the balanced, condition becomes,

\frac{X^{'}}{9} = \frac{50}{50} = 1 \Rightarrow X^{'} = 9 Ω

As, in series combinations resistances are added, so to get

9 Ω

at left gap the

3 Ω

resistance should be added in series with

X Ω (6 + 3 = 9 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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With a resistance of ‘X’ in the left gap and a resistance of 9 Ω in the right gap of meter bridge, the balance point is obtained at 40 cm from the left end. In what way and to which resistance 3Ω resistance be connected to obtained the balance at 50 cm from the left end?

Step-by-step Solution

With a resistance of ‘X’ in the left gap and a resistance of 9 $Ω$ in the right gap of meter bridge, the balance point is obtained at 40 cm from the left end. In what way and to which resistance $3 Ω$ resistance be connected to obtained the balance at 50 cm from the left end?