Find the equivalent resistance of the following combination

Find the equivalent resistance of the following combination

Solution

You need to know how to find cumulative resistance in case of resistors being attached in parallel and in series.

For series, Rnet = R1 + R2 + R3 and so on.

For parallel, 1 / Rnet = 1/ R1 + 1/ R2 + 1/R3 so on.

Now, for any given circuit you will have to identify the sections in which either of the above would be applicable, and then resolve the circuit to find the net resistance.

As for the given circuit, we can see that 40 and 70 ohm resistors are in parallel to each other while them being together in series with 30 and 60. That entire line is again in parallel with 10. The 20 ohm resistor is again in series with the the combination lying before it. We would begin with 40/70 line and resolve henceforth.

So net resistance of 40 and 70 ohm would be given as 1/ R = 1/40 + 1/70

or, R = 2800 / 110 = 280/11 = 25.4545 ohms

Now this R is in series with 30 and 60 ohm resistors. So, R1 = R + 30 + 60 = 90 + 25.4545 = 115.4545 ohms

Now this R1 is in parallel with 10 ohm resistor. So, R2 = 10 x 115.4545 / 125.4545 = 9.2029 ohms

Now this R2 is in series with 20 ohm resistor. So the net resistance would be equal to 9.2029 + 20 = 29.2029 ohms