Question

A wire of resistance $15\Omega$ is bent to form a regular hexagon ABCDEFA. Find the equivalent resistance of the loop between the points (a) A and B, (b) A and C and (c) A and D.

• A. (a) $3.08\Omega$; (b) $3.33\Omega$; (c) $3.75\Omega$
• B. (a) $2.08\Omega$; (b) $3.33\Omega$; (c) $3.75\Omega$
• C. (a) $4.08\Omega$; (b) $3.33\Omega$; (c) $6.75\Omega$
• D. (a) $5.08\Omega$; (b) $5.33\Omega$; (c) $3.75\Omega$

Answer 1

The correct option is B (a) $2.08\Omega$; (b) $3.33\Omega$; (c) $3.75\Omega$

Given Resistance of the wire$=15\Omega$

The resistance of each side of hexagon(R)$=\frac{15}{6}=2.5\Omega$

$\text{Part (a)}$

$R_{eq}=5RparallelR=\frac{5R}{6}=\frac{25}{12}=2.08\Omega$

$\text{Part (b)}$

$R_{eq}=4Rparallel2R=\frac{8R}{6}=\frac{40}{12}=3.33\Omega$

$\text{Part (c)}$

$R_{eq}=3Rparallel3R=\frac{3R}{2}=\frac{15}{4}=3.75\Omega$

Option $\text{B}$ is the correct answer.