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)

In the given circuit, $3\Omega$ and $7\Omega$
resistors are in series, hence equivalent resistance is
$R^{\prime }=R_1+R_2=3\Omega +7\Omega =10\Omega$
This $10\Omega$ resistor is in parallel with
$10\Omega$ resistance, hence equivalent resistance is
$\frac{1}{R^{\prime \prime }}=\frac{1}{10}+\frac{1}{10}=\frac{2}{10}$
$\Rightarrow R^{\prime \prime }=5\Omega$
This $5\Omega$ is in series with $5\Omega$ resistor
$R^{\prime \prime \prime }=5\Omega +5\Omega =10\Omega$
Now, this $10\Omega$ is in parallel with $10\Omega$ between $A$ and $B$.
Hence, equivalent resistance is
$\frac{1}{R_4}=\frac{1}{10}+\frac{1}{10}=\frac{2}{10}$
$\Rightarrow R_4=5\Omega$