Springs in Series and Parallel?

Aim

The aim of this laboratory experiment was to help the experimenter to setup as well as observe and verify Ohm’s law. Secondly, this laboratory experiment was meant to enable the experimenter verify the theory equations used to obtain the effective

resistance of parallel and series resistance.

Theory

Ohms law states that voltage is directly proportional to current in a conductive material. The constant of proportionality is called resistance. Resistance is the opposition offered to the flow of electrons in a conductive material. From ohms law the voltage across the load can be mathematically represented as

 

Where V is the voltage in volts and I is the current in amperes and R is the resistance. Introducing a constant of proportionality becomes. Current and voltage can be derived from the above equation as shown below

.

 

Resistors can be combine into parallel, series or a combination of the two. In series combination, the resistors are connected end to end to form only one path for electrons to flow through the circuit. The current is the same through each resistor and the total resistance can be obtained can be obtained by adding up the resistance value of the individual resistors. This is given by the equation:

……………………………..(4)

Figure 1: resistors in series

Resistors combined in parallel is whereby all the resistors are connected between the same set of electrically common points , that is, all tails connected together and all heads connected together. The current in the parallel circuit breaks up with some flowing along each parallel branch and recombine when the circuit meet again. The voltage in this configuration is the same, while the total resistance is obtained by adding up the reciprocal of each resistor value and obtaining the reciprocal of the total. This is given by the equation:

……………………………… (5)

Figure 2: resistors in parallel

Apparatus

1. Variable DC voltage source
2. Color coded resistors of various sizes
3. Variable resistor
4. Voltmeter
5. Ammeter
6. Connecting wire

Procedure

Procedure for Variation of current with voltage – constant resistance

The theoretical resistance of the resistance was obtained using the color codes and there values recorded in table 5.1. The experimental set up for the experiment was done as shown below.

Adjustment of the DC voltage source was done such that the smallest voltage readings were observed across resistor R. The resultant current and voltage readings were recorded in that 5.1. The above procedure was repeated with larger evenly spaced voltage values to obtain nine more values. Care was taken not to exceed the maximum stipulated voltage.

Procedure for Variation of current with resistance – constant voltage

Voltage provided by the instructor was recorded in table 5.2. This voltage were used for to resistors in all measurements. The experimental set up was done using the smallest color coded resistor. The circuit was switched on and the rheostat adjusted until the prescribed voltage was achieved. The current at this resistance (when the prescribed voltage had been achieved) was recorded in table 5.2. The previous steps were repeated with increasingly larger resistance until all the 9 rows of table 5.2 had been filled.

 Procedure for Variation of voltage with resistance – constant current

The current values provided by the instructor were recorded in table 5.3. The previous circuit was reconstructed starting with the smallest color coded resistance. The circuit was switched on and the rheostat adjusted until the prescribed current was achieved. The voltage at this resistance (when the prescribed voltage had been achieved) was recorded in table 5.3. The previous steps were repeated with increasingly larger resistance until all the 9 rows of table 5.3 had been filled.

Results

Table 5.1: Voltage and current reading for simple circuit

Resistance used ()
Trial	Voltage V (V)	Current I (mA)
1	1.107	0.015
2	1.153	0.016
3	1.216	0.017
4	1.249	0.017
5	1.287	0.018
6	1.314	0.018
7	1.356	0.019
8	1.432	0.020
9	1.510	0.021

 

Table 5.2: Voltage and current reading for simple circuit.

Voltage V (V)		1.2 V
Trial	Resistance R (ohms)	Current I (mA)
1	15	0.079
2	22	0.054
3	33	0.036
4	39	0.030
5	47	0.025
6	56	0.020
7	68	0.016
8	75	0.016
9	82	0.011

 

Table 5.3: Voltage and current reading for simple circuit.

Current I (mA)		0.035 mA
Trial	Voltage V (V)	Resistance R (ohms)
1	0.538	15
2	0.790	22
3	1.176	73
4	1.385	39
5	2.459	68
6	2.644	75
7	2.908	82
8
9

 

 

Analysis

Figure 1: A graph of Voltage (V) against current (I) for a constant resistor.

From the equation of the graph, where 67.485 is the slope of the graph. Using the concept of Ohms law, the slope of the graph of voltage against current is equal to the effective resistance of the constant resistor used, which is 68𝛺

The percentage difference between the slope and the constant resistance is calculated as shown below

 

 

Figure 2: A graph of resistance against reciprocal of current (I) for a constant voltage.

From the equation of the graph, where 0.9204 is the slope of the graph. Using the concept of Ohms law, the slope of the graph of resistance against reciprocal of current is equal to the effective constant voltage used, which is 1.2V.

The percentage difference between the slope and the constant resistance is calculated as shown below

 

 

Figure 3: A graph of voltage against resistance for a constant current.

From the equation of the graph, where 0.0293 is the slope of the graph. Using the concept of Ohms law, the slope of the graph of voltage against resistance is equal to the effective constant current used, which is 0.035A.

The percentage difference between the slope and the constant resistance is calculated as shown below

 

 

 

Discussion and Conclusion

This laboratory experiment was a success since the experimenter was able to setup as well as observe and verify Ohm’s law using the experimental data values. The experimental constant resistance was found to be. It had a percentage difference of 0.7% when it was compared to the expected constant resistance. The experimental constant voltage was found to be. It had a percentage difference of 23% when it was compared to the expected constant voltage. The experimental constant current was found to be. It had a percentage difference of 17% when it was compared to the expected constant current.

The presence of percentage difference implies presence of errors in the experimental data. Some of the sources of errors include use of uncalibrated voltmeter and ammeter, an assumption that there is no resistance in the connecting wires and other human errors such as inaccurate recording of data.

If these experiment was to be repeated in future, the following should be put in place so has to minimize experimental errors. The voltmeter and ammeter should be properly calibrated before use, the internal resistance of the voltmeter and ammeter should not be accounted for. Care should also be taken to ensure that the correct data is recorded in the data tables.