Question

Calculate the equivalent resistance of the given circuit diagram.

Answer 1

Given Data:

Left resistor = 3 Ω

Middle resistor = 5 Ω

Right resistor = 2 Ω

Two upper resistors = 10 Ω each

1. Simplify the upper branch:

The two 10 Ω resistors in the triangular upper branch are connected end-to-end in a series combination:

R₁ = 10 Ω + 10 Ω

= 20 Ω

Now, this simplified 20 Ω branch is connected across the same common junctions in a parallel combination with the central 5 Ω resistor.

Let the equivalent resistance of this parallel network be R_p:

`1/R_p = 1/20 + 1/5`

`1/R_p = 1/20 + 4/20`

`1/R_p = 5/20`

`1/R_p = 1/4`

R_p = 4 Ω

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

Since the initial 3 Ω resistor, the simplified central parallel network (R_p = 4 Ω), and the final 2 Ω resistor are all connected consecutively in a series combination:

R_AB = 3 Ω + 4 Ω + 2 Ω

= 9 Ω

The total equivalent resistance of the given circuit between points A and B is 9 Ω.