Question

When all the resistances in the circuit are $1\Omega$ each, then the equivalent resistance across points $A\&B$ will be:

• A. $5/6\Omega$
• B. $1/2\Omega$
• C. $2/3\Omega$
• D. $1/3\Omega$

Answer 1

The correct option is D $1/3\Omega$

Here at point "A" the three 1$\Omega$ resistance is divided therefore it is in parallel connection so we have to find it's equivalent.
$R_{equivalent}$ of upper portion at point "A" =$\frac{1}{3}$.
Also,at point "B" two 1$\Omega$ resistance is in parallel so we have to find it's equivalent.
$R_{equivalent}$ of lower portion "B"=$\frac{1}{2}$.
after finding the $R_{equivalent}$ of both the point "A" and "B" we combine it in series to find the final equivalent of circuit across "AB" which is equal to
$R_{equivalent}$=$\frac{1}{3}+\frac{1}{2}$=$\frac{5}{6}$.