Question

Deduce the expression for the equivalent resistance of the parallel combination of three

resistors R1, R2 and R3.

Consider the following electric circuit :

(a) Which two resistors are connected in series?

(b) Which two resistors are connected in parallel?

(c) If every resistor of the circuit is of 2 Ω, what current will flow in the ci​

Answer 1

Consider the following parallel circuit shown below: Let I1, I2 and I3 be the current flow through the resistor R1, R2 and R3 connected in parallel. Using Ohm’s law, current through each resistor is

I1 = V/R1, I2 = V/R2 and I3 = V/R3

Let their equivalent resistance be Rp then

V = I Rp ⇒ I = V/Rp

Total current through the circuit is

(a) R5 and R4 with Parallel combination of R2 and R3 are in series

(b) R2 and R3 are in parallel.

(c) R2 and R3 in parallel gives Rp = 1 Ω Rp, R5 and R4 are in series.

So, Req = 5 Ω R1 is not to be taken as it is shorted.

Current flowing, l = V/R = 5/5 = 1A