Question

Study the figure carefully.

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

Answer 1

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

There are two paths between D and B.

Path 1: D-A-B (resistors in series)

\[ \mathrm{R}_{1} = 10 + 8 \]

\[ = 18 \ \Omega \]

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

\[ \mathrm{R}_{2} = 4 + 5 \]

\[ = 9 \ \Omega \]

These two paths are in parallel, so:

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

\[ = \frac{1}{18} + \frac{1}{9} \]

\[ = \frac{1 + 2}{18} \]

\[ = \frac{3}{18} \]

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

\[ \therefore \mathrm{R}_{p} = 6 \ \Omega \]