Question

The resistors are connected as shown in the figure below. Find the equivalent resistance between the points A and B.

• A. $205\Omega$
• B. $10\Omega$
• C. $3.5\,\Omega$
• D. $5\,\Omega$

Answer 1

Answer: (D)

$5\,\Omega$

Answer 2

In the given circuit, $3\Omega$ and $7\Omega$ resistors are in series, hence equivalent resistance is $R'={{R}_{1}}+{{R}_{2}}=3\Omega +7\Omega =10\,\Omega$ This $10\,\Omega$ resistor is in parallel with $10\,\Omega$ resistance, hence equivalent resistance is $\frac{1}{R''}=\frac{1}{10}+\frac{1}{10}=\frac{2}{10}$ $\Rightarrow$ $R''=5\Omega$ This $5\Omega$ is in series with $5\Omega$ resistor $R'''=5\Omega +5\Omega =10\Omega$ Now, this $10\,\Omega$ is in parallel with $10\,\Omega$ between A and B. Hence, equivalent resistance is $\frac{1}{{{R}_{4}}}=\frac{1}{10}+\frac{1}{10}=\frac{2}{10}$ $\Rightarrow$ ${{R}_{4}}=5\Omega$