Question

In the figure, calculate equivalent resistance between points (a) A and B (b) B and C (c) A and C.

Answer 1

(a) Resistances of 4 Ω and 12 Ω are connected in parallel between points A and B.

Let \(\mathrm{R}_{p_1}\) be their equivalent resistance.

\[ \frac{1}{\mathrm{R}_{p_1}} = \frac{1}{4} + \frac{1}{12} \]

\[ = \frac{3 + 1}{12} \]

\[ = \frac{4}{12} \]

\[ = \frac{1}{3} \]

\[ \mathrm{R}_{p_1} = 3 \ \Omega\]

(b) Resistances of 12 Ω, 24 Ω and 8 Ω are connected in parallel between points B and C.

Let \(\mathrm{R}_{p_2}\) be their equivalent resistance.

\[ \frac{1}{\mathrm{R}_{p_2}} = \frac{1}{12} + \frac{1}{24} + \frac{1}{8} \]

\[ = \frac{2 + 1 + 3}{24} \]

\[ = \frac{6}{24} \]

\[ = \frac{1}{4} \]

\[ \mathrm{R}_{p_2} = 4 \ \Omega\]

(c) Now, equivalent resistance \(\mathrm{R}_{p_1}\) is in series with equivalent resistance \(\mathrm{R}_{p_2}\). Therefore, equivalent resistance between A and C \(\left(\mathrm{R}_{s}\right)\) is :

\[ \mathrm{R}_{s} = \mathrm{R}_{p_1} + \mathrm{R}_{p_2} \]

\[ = 3 + 4 \]

\[ = 7 \ \Omega\]