Question

The equivalent resistance between points $A$ and $B$ is

• A. $\frac{65}{2}\Omega$
• B. $\frac{45}{2}\Omega$
• C. $\frac{5}{2}\Omega$
• D. $\frac{91}{2}\Omega$

Answer 1

The correct option is B $\frac{45}{2}\Omega$

The equivalent circuit diagram shows that the series combinations of the resistances in the circuit are:
$15\Omega \&10\Omega ,40\Omega \&10\Omega ,30\Omega \&20\Omega$

We can name the points having same potential and rearrange as shown in the figure


The resistances $25\Omega ,50\Omega$ and $50\Omega$ are in parallel.
So, circuit can be rearranged as

Effective parallel resistance is given by $\frac{1}{R_P}=\frac{1}{25}+\frac{1}{50}+\frac{1}{50}$
$R_P=\frac{25}{2}\Omega$


Their effective resistance(parallel) is in series with $2\Omega$ and $8\Omega$.
$R_{\text{eq}}=2+\frac{25}{2}+8=\frac{45}{2}\Omega$