Question

Three resistors R1 ,R2 and R3 are connected in parallel and combination is connected to a battery and ammeter voltmeter and key. Draw suitable circuit diagram and obtain an expression for the equivalent resistance of the combination of the circuit

Answer 1

Given:

Three resistors R1, R2, and R3 connected in parallel.

The combination is connected to a battery and ammeter voltmeter and key.

To Find:

An expression for the equivalent resistance of the combination of the circuit

Solution:

Consider three resistors of resistances R1, R2, and R3 connected in parallel as shown in the diagram attached below.

A source of emf V is connected to the combination.

When resistors are in parallel, we know that the potential difference (V) across each resistor is the same.

Let a current I enter the combination. It gets divided into I1 I2 and I3.

We know that I = I1 + I2 + I3     - (1)

Using Ohm's Law,

I1 = V/R1

I2 = V/R2

I3 = V/R3

Let Req be the equivalent resistance of the circuit.

I = V/Req

Substituting the above values in equation 1 we get:

V/Req = V/R1 + V/R2 + V/R3

Taking V common from both sides and canceling we get:

1/Req = 1/R1 + 1/R2 + 1/R3

Thus when resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.