Question

Study the figure carefully.

What is the equivalent resistance in the figure when the current enters at A and leaves at D?

Answer 1

In the figure, current enters at A and leaves at D.

There are two paths between A and D.

Path 1: A to D directly

\[ \mathrm{R}_{1} = 6 \ \Omega \]

Path 2: A-B-C-D (resistors in series)

\[ \mathrm{R}_{2} = 3 + 2 + 1 \]

\[ = 6 \ \Omega \]

These two paths are in parallel, so:

\[ \frac{1}{\mathrm{R}_{p}} = \frac{1}{\mathrm{R}_{1}} + \frac{1}{\mathrm{R}_{2}} \]

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

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

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

\[ \therefore \mathrm{R}_{p} = 3 \ \Omega \]