Question

The total resistance between x and y in $\Omega$ is:

• A. $1\Omega$
• B. $4\Omega$
• C. $\left(4/3\right)\Omega$
• D. $\left(2/3\right)\Omega$

Answer 1

The correct option is C $\left(4/3\right)\Omega$

Consider the figure above.

In the figure, the $8\Omega$ and $2\Omega$ resistances have same end points, since no resistance lies between x and A. Hence They are in parallel. Hence resistance between AO is $\frac{16}{10}\Omega$.

With similar argument, $4\Omega$ and $6\Omega$ resistances are in parallel. Hence the resistance between BO is $\frac{24}{10}\Omega$.

These these two resistances found are joined end to end with O as their common point. So they are in series combination. Thus the equivalent resistance becomes $\frac{16}{10}\Omega +\frac{24}{10}\Omega =4\Omega$

Now this new equivalent resistance obtained, resistance AB, the equivalent resistance derived above and resistance xy are in parallel combination, each equal to $4\Omega$.

Hence the equivalent resistance of the circuit is $\frac{4}{3}\Omega$