**Contents**hide

## Introduction

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

### 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.

**5. R ****L/A, **where L= length and A = Area.

**R = ρL/A**, where ρ = resistivity of the conductor.

### Resistor Connected In Series

Resistors are connected in series if the same current flows in every resistor.

### Characteristics Of Resistor Connected In Series

1. The same current flows through the different resistors.

2. The sum of all potential differences in a circuit across the different resistors is the total potential difference of that circuit.

3. Resistance of a resistor is directly proportional to the voltage across that resistor.

4. The sum of individual resistance in a circuit is equal to the equivalent resistance of that circuit.

**R****eq ****= R****1 ****+ R****2**** + R****3.**

5. The value of equivalent resistance in a circuit is always greater than the value of individual resistance of that circuit.

### Uses of Series Resistor

1. Water heaters,

2. Refrigerators,

3. Well water pump,

4. For increasing resistance of a circuit,

5. For decreasing current in a circuit,

6. When there is a need for the less potential difference in a resistor.

## Aim

To determine the equivalent resistance of two or more resistors connected in series.

## 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 when there is only one path for the flow of current, i.e.; the same current flows across every resistor.

The sum of individual resistors is called the equivalent resistor.

**R****eq ****= R****1 ****+ R****2**** + R****3. **

## 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 **R****1, **** ****R****2****,**** R****3****.**

**Step 3.** Connect the resistors in series 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.

Resistor used | No. of observations | Voltmeter reading (in volt) V | Ammeter reading (in ampere), A | R = V/I
| Mean value of resistance (in ohm). |

R1 | (a) (b) (c) | R1 = (a + b+ c)/3 =……….ohm | |||

R2 | (a) (b) (c) | R2 = (a + b+ c)/3 =……….ohm | |||

R3 | (a) (b) (c) | R3 = (a + b+ c)/3 =……….ohm | |||

RS = R1 + R2 + R3 | (a) (b) (c) | Rs = (a + b+ c)/3 =……….ohm |

## 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 series combination.

1. From calculation R’s = ……..ohm

2. From experiment RS = ……….ohm

Difference in both the values Rs – R’s = ……….ohm.

## Result

1. There is significantly less difference between the measured value and experimental value of resistance.

2. The equivalent resistance of the circuit, RS = ……….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 series.

## Viva Questions With Answers

**Q.1 How can you find equivalent resistance in a circuit when resistors are connected in series?**

ANS. By adding all the individual resistance, R = R1 + R2 + R3.

**Q.2 Name the SI unit of resistance?**

ANS. Ohm

**Q.3 What is the benefit of connecting wires in series?**

ANS. In order to obtain higher resistance, we connect wires in series.

**Q.4 Why are the standard resistances made up of manganin?**

ANS. Manganin has higher thermal stability, and there is no change in resistance with the change of temperature.

**Q.5 Connecting wires are made up of copper. Describe this sentence.**

ANS. Copper wire let the current pass through the circuit without much resistance. Therefore connecting wires are made up of copper.

**Q.6 On what properties of wire resistance depend?**

ANS. Length, area and nature of conducting wire.

**Q.7 If the two resistors of resistance 7Ω and 5Ω are connected in series, what is the circuit’s equivalent resistance?**

ANS. 7Ω + 5Ω = 12Ω.

**Q.8 What is a rheostat?**

ANS. This device is used to control the flow of current in a circuit by changing its resistance.

An Indian physicist and astronomer.

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