Twelve 1 Ω resistors are used as edges to form a cube. The $R_{ eq }$ seen between the two diagonally opposite corners of cube is

(a) $\frac{6}{5}$ Ω (b) $\frac{5}{6}$ Ω (c) 6 Ω (d) $\frac{5}{12}$ Ω

Question

Twelve 1 Ω resistors are used as edges to form a cube. The [latex] R_{ eq } [/latex] seen between the two diagonally opposite corners of cube is

(a) [latex] \frac{6}{5}[/latex] Ω (b) [latex] \frac{5}{6} [/latex] Ω (c) 6 Ω (d) [latex] \frac{5}{12} [/latex] Ω

Accepted Answer

The equivalent circuits is

Applying KVL, we get

[latex] \begin{gathered} V-\frac{I}{3} R-\frac{I}{6} R-\frac{I}{3} R=0 \ V=I\left\lgroup \frac{R}{3}+\frac{R}{6}+\frac{R}{3} ight group=I \frac{5 R}{6} \ \Rightarrow \frac{V}{I}=R_{ eq }=\frac{5}{6} \Omega \end{gathered} [/latex]

Chapter 1

Q. 1.P.12

Q. 1.P.12

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