Question

Find the equivalent resistance between points A and B of the network shown below.

• A. $6\Omega$
• B. $7\Omega$
• C. $4\Omega$
• D. $10\Omega$

Answer 1

The correct option is B $7\Omega$

The three $3\Omega$ resistances present in the middle are parallel to one another.
Hence, their effective Resistance $R_p$ can be calculated as:
$\frac{1}{R_p}=\frac{1}{3\Omega }+\frac{1}{3\Omega }+\frac{1}{3\Omega }$
$\Rightarrow \frac{1}{R_p}=\frac{3}{3\Omega }$
$\Rightarrow R_p=\frac{3\Omega }{3}=1\Omega$.
This $1\Omega$ is in series with the other $1\Omega$ and $5\Omega$ resistors.
Hence, the equivalent resistance becomes $1\Omega +1\Omega +5\Omega =7\Omega$.