Find the equivalent resistance between points A and B shown

Find the equivalent resistance between points A and B shown in the figure below, where R_1=1.4 ohm and R_2=3.5 ohm.

Here we need to know that for resistors connected in series, the net resistance is given as:

Rnet = R1 + R2 + R3 and so on.

While for resistors connected in parallel the net resistance is given as: 1 / Rnet = 1/ R1 + 1/R2 + 1/R3 and so on.

We will make use of the above to solve the given problem.

The resistor R2 is in parallel with 4.8 and 8.2 ohm resistors which together are in series with 6.3 ohm resistor.

The above combination is again in parallel with 2.5 Ohm resistor and R1.

So the net resistance of the left most branch would be: 6.3 + 4.8 x 3.5 x 8.2 / (4.8x3.5 + 3.5x8.2 + 4.8x8.2)

= 6.3 + 137.76 / 84.86 = 7.92 Ohms

Hence the net resistance of the circuit = 7.92 x 2.5 x 1.4 / (7.92 x 2.5 + 2.5 x 1.4 + 7.92 x 1.4)

= 27.72 / 34.388 = 0.8061 Ohms

Therefore the require resistance between points A and B is 0.8061 Ohms