Introduction

In this science experiment, we will learn to determine the equivalent resistor of two or more resistors in parallel.

Resistance

1. The property of a conductor to resist the flow of current is called the resistance of that conductor.
2. According to ohm’s law, Potential difference = Electric Current/ Resistance.

V = IR 

R = V/I

Therefore, the ratio of potential difference and electric current is called resistance.
3. The SI unit of resistance is ohm or volt/ampere.
4. The resistance of a conductor depends upon the area, length and material of that conductor.
R ∝ L/A, where L= length and A = Area.
R = ρL/A, where ρ = resistivity of the conductor.

Resistors Connected In Parallel

Resistors are connected in parallel if the same potential difference exists across all the resistors.

Resistors are connected in parallel.

Characteristics Of Resistor Connected In Series

1. Same potential difference across every resistor.
2. The sum of the current in each resistor is the total current of the equivalent resistor.

I = I1 + I2 + I3.

3. The current in the resistor is inversely proportional to the resistance, i.e. I α 1/R.
4. The equivalent resistance of the circuit,

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

5. The circuit’s equivalent resistance is smaller than the value of the least resistor in the circuit.

Uses Of Parallel Resistor

1. Lighting fixtures,
2. Power supply,
3. Electrical points in the house,
4. For decreasing resistance in the circuit,
5. For increasing current in the circuit.

Aim

To determine the equivalent resistor of two or more resistors connected in parallel.

Apparatus Required

1. Ammeter,
2. Voltmeter,
3. One-way plug key,
4. Connecting wire,
5. Two standard resistance coils,
6. Low resistance rheostat,
7. Cell or battery eliminator.

Theory

Resistors are connected in series if the potential difference across each resistor is equal to the potential difference of the circuit.

 (1/Req = 1/R1 + 1/R2 + 1/R3)

Circuit Diagram

Procedure

Step 1. Connect the devices as shown in the figure, leaving one unknown resistor.

Step 2. Using Ohm’s law, find the value of each resistor R1,  R2, R3.

Step 3. Connect the resistors in parallel across the ends of the voltmeter, as shown in the above figure.

Step 4. Plug the key on the battery eliminator.

Step 5. Take the readings of the ammeter and voltmeter.

Step 6. Repeat steps  4 and 5 by taking different values of sliding contact of the rheostat.

Step 7. Note down all your readings in the table and find the ratio of V and I of each resistor for finding equivalent resistance.

Observation Table

Observation

1. Least count of ammeter = ……..
2. Least count of voltmeter =……..
3. Zero error of voltmeter = ……..
4. Zero error of ammeter = …….

Calculations

1. Mean value of R1 = …….. Ohm.
2. Mean value of R2 = ………Ohm.
3. Mean value of R3 = ……….Ohm.

The equivalent resistance of parallel combination.

1. From calculation R’p = ……..ohm
2. From experiment Rp = ……….ohm

Difference in both the values Rp – R’p = ……….ohm.

Result

1. There is not much difference between the measured value and the experimental value of the resistance connected in parallel.
2. The equivalent resistance of the resistors connected parallel, Rp = ……….ohm.

Percentage Error

Percentage error
=  (Experimental value – Calculated value)/Calculated value X 100
= (Rs – R’s)/R’s X 100
= ……………%

Precautions

1. Zero error should be measured correctly.
2. Note the value of least count correctly.
3. There should be no defects in devices.
4. Area of the wire should be more as it offers the minimum resistance.
5. Rheostat must be of the low range.
6. The ends of the wire should be connected to the terminals of the voltmeter.
7. Positive terminal of the cell should be connected to the positive terminal of the voltmeter or ammeter.
8. Don’t allow the current to flow longer in the wire because it can heat up.

Sources of Error

1. While observing the devices, reading errors may occur.
2. Wire may heat up due to the flow of current for a longer period of time.
3. Area of wire may not be uniform.
4. The screws may not be adequately tightened.
5. The terminals of the cell may be connected to the wrong terminal of devices.

Conclusion

From the above experiment, we have learnt to determine the equivalent resistor of two or more resistors connected in parallel.

Viva Questions With Answers

Q.1 Name the quantity which remains the same in a parallel resistor.

ANS. Potential difference.

Q.2 Why is there a decrease in total resistance when resistors are connected in parallel?

ANS. Because area increase in parallel resistors, and resistance is inversely proportional to area. Therefore area increases and potential decreases.

Q.3 What is the direction of current in a circuit?

ANS. From the positive terminal of the cell to the negative terminal.

Q.4 If the parallel resistance of two resistors changes to the series resistance of two resistors, how many times does the equivalent resistor change?

ANS. The equivalent resistance of two resistors connected parallel RP = R/2,

And the equivalent resistance of two resistors connected in series RS = 2R,

RS = 4RP

Therefore, resistance increases by four times.

Q.5 What is the range of ammeter?

ANS. The range of the ammeter is the maximum value of current it can measure.

Q.6 Household appliances are connected in a series combination or a parallel combination?

ANS. Parallel combination

Q.7 How the resistance of a circuit depends upon its area?

ANS. Resistance is inversely proportional to the area.

Q.8 Why do we connect wires in series?

ANS. In order to obtain minimum resistance and maximum current.

Q.9 What is the difference between resistance and resistor?

ANS. A resistor is a device to measure resistance in a circuit, while resistance is the property of conducting wires to resist current.

Q.10 What was the aim of our experiment?

ANS. To determine the equivalent resistor of two or more resistors connected in parallel.

Vikram Sarabhai

An Indian physicist and astronomer.