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
$\frac{1}{R_{4}}=\frac{1}{10}+\frac{1}{10}=\frac{2}{10}$
$\Rightarrow R_{4}=5 \,\Omega$