CUET · PHYSICS · PYQ PAPER 2023

A uniform metallic wire of resistance \(4 \Omega\) is bent to form a circle. What is the effective resistance between the end of its diameter?

A \(1 \Omega\)
B \(2 \Omega\)
C \(4 \Omega\)
D \(8 \Omega\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(1 \Omega\)

Step-by-step Solution

Detailed explanation

\(R_{semicircle} = \frac{R_{total}}{2} = \frac{4 \Omega}{2} = 2 \Omega\) \(R_{eff} = \frac{R_{semicircle} \times R_{semicircle}}{R_{semicircle} + R_{semicircle}} = \frac{2 \Omega \times 2 \Omega}{2 \Omega + 2 \Omega} = 1 \Omega\)

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.

Same subject

Match List-I with List-II

List-I (AC circuit)	List-II (Features)
(A) Only resistor in a circuit	(I) Current leads or lag the voltage
(B) Only capacitor in a circuit	(II) Voltage and Current are in phase
(C) Only inductor in a circuit	(III) The current lags the voltage by \(\frac{\pi}{2}\)
(D) Series LCR circuit \(X_C \neq X_L\) and \(R \neq 0\)	(IV) The current leads the voltage by \(\frac{\pi}{2}\)

Choose the correct answer from the options given below :

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