Question

Three resistors R₁, R₂, R₃ are to be combined as shown in the figure.

1. Identify the series and parallel combinations.

2. Which combination has lowest resistance. Arrive at the expression for the effective resistance of this combination.

Answer 1

1. Fig(i) – parallel

Fig. (ii) – series 

2. Fig. (i)

Let V be the potential between A and B.

I = I₁ + I₂ + I₃

and applying Ohm’s law to R₁, R₂ and R₃ we get,

V = I₁R₁,V = I₂R₂,V = I₃R₃

So that

I = I₁ + I₂ + I₃ = V\(\Big(\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\Big)\)

An equivalent resistance R_eq that replace the combination, and hence

\(\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\)