Question

Calculate the equivalent resistance between points A and B in the given circuit diagram.

Answer 1

Given:

Left series resistor = 5 Ω

Right series resistor = 6 Ω

The network between the two middle junctions consists of:

Top branch = 4 Ω + 4 Ω + 4 Ω = 12 Ω

Middle branch = 4 Ω

Bottom branch = 2 Ω + 2 Ω + 2 Ω = 6 Ω

These three branches are connected in parallel.

1. Calculation of the equivalent resistance of the parallel network (R):

Using the parallel combination formula:

`1/R = 1/12 + 1/4 + 1/6`

Taking LCM = 12,

`1/R = 1/12 + 3/12 + 2/12`

`1/R = (1 + 3 + 2)/12`

`1/R = 6/12`

`1/R = 1/2`

R = 2 Ω

2. Calculation of the total equivalent resistance (R_AB):

Since the 5 Ω resistor, the simplified parallel network of 2 Ω and the 6 Ω resistor are connected consecutively in a series combination:

R_AB ​= 5 Ω + 2 Ω + 6 Ω

= 13 Ω

The total equivalent resistance between points A and B is 13 Ω.