Question

Calculate the equivalent resistance between points

1. B and E
2. A and F.

Answer 1

(a) Between B and E, resistances of 1 Ω, 2 Ω and 3 Ω (B-C-D-E) are in series.

\[ \mathrm{R}_{s} = (1 + 2 + 3) = 6 \ \Omega \]

\(\therefore\) Equivalent resistance of \(\mathrm{R}_{s}\) and 3 Ω (BE) in parallel

\[ \frac{1}{\mathrm{R}_{p}} = \frac{1}{6} + \frac{1}{3} \]

\[ = \frac{1 + 2}{6} \]

\[ = \frac{3}{6} \]

\[ = \frac{1}{2} \]

\[ \mathrm{R}_{p} = 2 \ \Omega\]

(b) Between A and F, resistance of 3 Ω (AB), \(\mathrm{R}_{p}\) and 3 Ω (EF) are in series.

\[ \mathrm{R} = 3 + \mathrm{R}_{p} + 3 \]

\[ = 3 + 2 + 3 \]

\[ = 8 \ \Omega\]