WBJEE · Physics · Current Electricity

Six wires, each of resistance \(r\), are connected so as to form a tetrahedron. The equivalent resistance of the combination when current enters through one corner and leaves through some other corner is

A \(r\)
B \(2 r\)
C \(\frac{r}{3}\)
D \(\frac{r}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{r}{2}\)

Step-by-step Solution

Detailed explanation

Six wires each of resistance \(r\) form a tetrahedron as shown in the following figure It is circuit of Wheatstone the equivalent resistance of upper circuit \(\frac{1}{R}=\frac{1}{2 r}+\frac{1}{2 r}=\frac{2}{2 r}=\frac{1}{r}\) \[ R=r \] It will in parallel with outer resistance…

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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