COMEDK · Physics · 19. Current Electricity

A battery of emf 12 V and negligible resistance is connected across the diagonally opposite corners of a cubical network consisting of 12 resistors each of resistance \(2 \Omega\). The equivalent resistance of the network is

A \(\frac{1}{2} \Omega\)
B \(\frac{4}{3} \Omega\)
C \(\frac{1}{4} \Omega\)
D \(\frac{5}{3} \Omega\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{5}{3} \Omega\)

Step-by-step Solution

Detailed explanation

In a closed loop, say \(A B C C^{\prime} E A\) and apply Kirchhoffs second rule, \(-I R-\left(\frac{I}{2}\right) R-I R+\varepsilon=0\) where, \(R\) is the resistance of each edge and \(\varepsilon\) the emf of battery. Thus, \(\varepsilon=\frac{5}{2} I R\) The equivalent…

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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