AIM
To determine of the equivalent resistance of two resistors when connected in series.
MATERIALS REQUIRED
Two standard resistance coils, ammeter, voltmeter, one - way plug key, low resistance rheostat, connecting wires, cell or battery eliminator.
THEORY
When two or more resistors are connected end to end, then they provide only one path to the flow of current i.e., the same current flow through each resistor. Then, they are in series combination.
V = V1 + V2
let v be the applied potential difference by a dc source across the combination of unknown resistors R1 and R2.
According to ohms law, for each resistor,
V1 = IR1, V2 = IR2
Then the equivalent resistance of the series combination of two resistors is given by
Rs = R1 + R2
Circuit Diagram
Apparatus Arrangement:
PROCEDURE
1. Join the circuit as shown in the circuit diagram or apparatus arrangement with one of the unknown resistors.
2. Find the values of two given unknown resistors R1 and R2 one by one.
3. Tabulate at least three readings of ammeter and voltmeter for the given unknown resistor.
4. By using Ohm’s law, find the value of each resistance.
5. Connect the given resistors in series combination between the terminals of voltmeter as shown in the figure above
6. Plug in the one - way plug key and note the readings of ammeter and voltmeter in the observation table.
7. Repeat the step 6 three times by changing the position of the sliding contact of the rheostat
8. Write the readings and find the ratio of V and I. It will give the equivalent resistance of the combination.
OBSERVATION TABLE
Resistor used |
No. of observations |
Voltmeter reading ‘V’ (in volt) |
Ammeter reading ‘I’ (in ampere) |
Resistance (in ohm) |
R1 |
(a) (b) (c) |
0.20 0.40 0.65 |
0.1 0.2 0.3 |
2.0 2.0 2.2 |
R2 |
(a) (b) (c) |
0.40 0.80 1.25 |
0.1 0.2 0.3 |
4.0 4.0 4.2 |
RS = R1 + R2 |
(a) (b) (c) |
0.55 1.25 1.85 |
0.1 0.2 0.3 |
5.5 6.2 6.2 |
OBSERVATIONS
1. Least count of ammeter:
The image of the ammeter is attached here:
The range of the ammeter =500 - 0 mA = 500 mA = 0.5 A
The number of divisions in between two consecutive values= 10
Therefore, the least count = 
= 0.01 A
2. Zero error of ammeter:
The needle of the ammeter points towards zero of the main scale of the ammeter, therefore no zero error .
3. Least count of voltmeter:
The range of voltmeter = 2 - 0 V= 2 V.
The number of division in small scale between two division on the main scale
= 10
Therefore, the least count
4. Zero error of voltmeter = 0 V.
CALCULATIONS
Resistance |
no. of observation |
Resistance R(ohm) |
Mean Resistance R(ohm) |
R1 |
(a) (b) (c) |
2.0 2.0 2.2 |
2.06 |
R2 |
(a) (b) (c) |
4.0 4.0 4.2 |
4.06 |
Rs = R1 + R2 |
(a) (b) (c) |
5.5 6.2 6.2 |
5.9967 |
1. Mean value of R1 = 2.06 Ω
2. Mean value of R2 = 4.06 Ω
Equivalent value of series combination:
(a) by calculation, = 2 Ω + 4 Ω = 6 Ω
(b) by experiment, = 5.99 Ω
Difference in both value = Rexp – Rcalculated= 0.01 Ω
RESULT
1. The calculated and the experimental value of equivalent resistance are similar. Hence Rs = R1 + R2 is verified.
2. The equivalent resistance, Rs = 5.99 Ω
PERCENTAGE ERROR
Percentage error = 
= 0.16667 %
PRECAUTIONS
1. Remove the oxide layer from the ends of connecting wires by rubbing it with sandpaper.
2. All connections should be kept tight and properly done as per the circuit diagram.
3. Take out the plug from the plug key in between the two observations to avoid heating.
4. A low resistance rheostat should be used in the circuit to obtain a large variation in current.
5 A thick copper connecting wire should be used in the circuit.