Question

obtain an expression for effective resistance in series combination of resistors of three resistor

Answer 1

Answer:

A circuit is said to be in a parallel connection when the resistors are connected in such a way that they branch out from one point. The potential difference in a parallel circuit is the same for each resistor and the current flow is not the same for all resistors. The total current flow through the circuit is calculated by summing up the current flow through each resistor. Parallel circuit connections find application in household electric distribution. The reason why a parallel circuit is preferred is to avoid short circuits and to monitor the flow of current for different devices. The other type of circuit is a series connection. Below is an experiment to determine the equivalent resistance when the resistors are connected in parallel.

Aim

To determine the equivalent resistance of two resistors when connected in parallel.

Theory

If the resistors are connected in parallel along with a battery, then the total current I is calculated as a sum of the separate value of current through each branch. It is given as:

I = I1+I2+I3+….

Materials Required

A battery

A plug key

Connecting wires

An ammeter

A voltmeter

Rheostat

A piece of sandpaper

Two resistors of different values

Procedure

Make all the connections as shown in the experimental setup I by keeping the key off.

Insert the key when the circuit is connected appropriately.

For resistors R1 and R2, note three readings of ammeter and voltmeter.

Connect the circuit as shown in the experimental setup II.

Resistors and voltmeter both are connected in parallel.

Record three different readings of ammeter and voltmeter and also use a rheostat.

Remove the key.

With the help of the observation table, do the calculations.

Observation Table

Resistor used No.of observations Voltmeter reading in Volts (V) Ammeter reading in Ampere (I) R=V/I (in Ohm) Mean value of resistance (Ohm)

R1 (first resistor) a 0.01 0.01 1 R1 = 1 ohm

b 0.02 0.02 1

c 0.04 0.04 1

R2 (second resistor) a 0.02 0.01 2 R2 = 2 ohm

b 0.06 0.03 2

c 0.08 0.04 2

1/Rp=(1/R1)+(1/R2)

Parallel combination

a 0.026 0.04 0.67 Rp=0.67 ohm

1/Rp=1.5 ohm

Result

The calculated value of 1Rp 1Rp=(1R1)+(1R2)=1.5Ω

The experimental value of 1Rp 1Rp=1.5Ω

The equivalent resistance Rp is less than the individual resistance.