Question

Find the equivalent resistance of the network shown in figure between the points P and Q.

• A. $30\Omega$
• B. $\frac{10}{3}\Omega$
• C. $10\Omega$
• D. $\frac{3}{10}\Omega$

Answer 1

The correct option is B $\frac{10}{3}\Omega$

Even though there are branches with no resistors, you can see that no resistor gets bypassed by these zero resistance paths. Current must flow through all 10Ω resistors. But how exactly? This combination can be simplified fairly easily. For all such questions, you can do it the same way. Mark out all the points P and Q as shown. You will notice that all junctions that are at the same potential can be marked as the same point.

Now I can rearrange the circuit as follows.
Mark out two points P and Q. Then connect the terminals of all devices connected to them. I get $R_A$ is connected between P and Q. $R_B$ also has its terminals connected to P and Q, and so does $R_C$.
Thus we get,

This is just 3 10$\Omega$ resistors in parallel. You get the equivalent resistance as $\frac{10}{3}\Omega$.