3 Nisan 2013 Çarşamba

PARALLEL AND SERIES SIMPLE ELECTRIC CIRCUITS


(National Curriculum Reference: 10.2.3.1)

EQUIPMENT: 
Power supply, voltmeter, ammeter (digital multimeter), resistances with different values, connection cables.

PURPOSE OF THE EXPERIMENT:
To investigate the differences between parallel and series circuits by constructing series and parallel circuits and calculating the values of each resistance and equivalent resistance by using the values read from ammeter and voltmeter. In other words, the aim is learning about current flow and the operational differences between series and parallel circuits.

PROCEDURE:
·         PART 1: SERIES CIRCUIT
In this part we constructed the circuit by connecting the resistances in series as shown in Figure 1. Then we recorded the values of resistances as   to the column labeled ‘accepted’ into Calculation Table 1.

 

Figure1. Experimental Setup for Part 1





Accepted
Calculated
Absolute Error
Relative Error (%)
R1 (Ω)
10,4Ω
10,31Ω
0,01
0,9%
R2 (Ω)
33,2Ω
31,85Ω
0,04
3,9%
  R3 (Ω)
16,5Ω
16,10Ω
0,02
2,0%
Req(Ω)
59,4Ω
59,74Ω
0,01
1,0%

Table1. Calculation Table for Part 1


Then we adjusted voltage to 12V DC and then switch on the power supply and read the value on ammeter and recorded it into Measurement Table 1. We measured the current values at points A, B, C and D separately. Then we measured the values of by using voltmeter and record into Measurement Table 1. Then we turned off the power supply.



V (V)

I (A)
Between A - B
2,000 (V)
At point A
0,194 (A)
Between B - C
6,243 (V)
At point B
0,196 (A)
Between C - D
3,172 (V)
At point C
0,197 (A)
Between A - D
11,46 (V)
At point D
0,193 (A)

Table2. Measurement Table for Part 1

Then we calculated the R values due to Measurement Table 1 and then record these values into Calculation Table 1.

We used the formula shown below.
 

·         PART 2: PARALLEL CIRCUIT

In this part we constructed the circuit shown in Figure 2 by connecting the resistances in parallel. Then we recorded the values of the resistances as and  to the column labeled ‘accepted’ into Calculation Table 2. We used resistors with different values.
 
Figure2. Experimental Setup for Part 2




Accepted
Calculated
Absolute Error
Relative Error (%)
R1  (Ω)
10,4 Ω
10,22 Ω
0,017
1,73 %
  R2 (Ω)
32,4 Ω
31,42 Ω
0,030
3,02 %
  Req (Ω)
8,0 Ω
7, 96 Ω
0,005
0,50 %

Table3. Calculation Table for Part 2


 
Then we adjusted the voltage value to 12V and turned on the power supply. We measured the potential difference between points A and B,Vab , and record it into Measurement Table 2. We repeated this for Vcd, Vef  and record it into Measurement Table 2 shown below.



V (V)

I (A)
Between A - B
11,35 (V)
At point A
1,11 (A)
Between C - D
11,31 (V)
At point C
0,36 (A)
Between E - F
11,30 (V)
At point E
1,42 (A)
-           
-           
At point F
1,42 (A)

Table4. Measurement Table for Part 2


Then we read the values of  through ammeter and record them into Measurement Table 2. Finally we turned off the power supply.

Then we calculated the R values due to Measurement Table for Part 2 and then record these values into Calculation Table for Part 2.

We used the formula shown below.
 


In computation part: 

-          By using the values of V and I in Measurement Tables, we calculated the values of resistances and recorded the values we found into the column labeled ‘calculated in the experiment’ in Calculation Tables.

We also calculated the equivalent resistance of the circuits and recorded the calculated values into the column labeled ‘accepted’ in Calculation Tables.


-          Then we calculated absolute errors by comparing the values in ‘calculated in the experiment’ and ‘accepted’ columns and recorded them into the tables.

We also calculated the relative errors here and recorded them into the tables.



Accepted
Calculated
Absolute Error
Relative Error (%)
R1 (Ω)
10,4Ω
10,31Ω
0,01
0,9%
R2(Ω)
33,2Ω
31,85Ω
0,04
3,9%
  R3 (Ω)
16,5Ω
16,10Ω
0,02
2,0%
Req (Ω)
59,4Ω
59,74Ω
0,01
1,0%

Table1. Calculation Table for Part 1



Accepted
Calculated
Absolute Error
Relative Error (%)
R1  (Ω)
10,4 Ω
10,22 Ω
0,017
1,73 %
  R2 (Ω)
32,4 Ω
31,42 Ω
0,030
3,02 %
  Req (Ω)
8,0 Ω
7, 96 Ω
0,005
0,50 %

Table3. Calculation Table for Part 2


THE RESPONSES TO THE QUESTIONS:
PART 1: SERIES CIRCUIT
 


*The total resistance of the circuit is equal to the sum of the individual resistances.

 



PART 2: PARALLEL CIRCUIT
 


CONCLUSION:
          A series circuit is a circuit in which resistors are arranged in a chain, so the current has only one path to take. The current is the same through each resistor. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors: Equivalent resistance of resistors in series :
R = R1 + R2 + R3 + ...
(http://physics.bu.edu)
 
          A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together. The current in a parallel circuit breaks up, with some flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistor in parallel is the same. The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total; equivalent resistance of resistors in parallel:
1 / R = 1 / R1 + 1 / R2 + 1 / R3 +...
 (http://physics.bu.edu)
The experiment was about series and parallel circuits. The objectives were to determine the total current and voltage for series and parallel circuits and observing the relationship of the total voltage and the voltage in each resistor for series and parallel circuits. Moreover, we determine the relationship of the total current and the current in each resistor for series and parallel circuits. These were achieved by computing and analysing the data gathered and the numerical results obtained from using Ohm's Law to calculate the resistance in a circuit are close enough to the accepted values to validate this experiment.
In electrical circuits there is a relationship between current, voltage, resistance, and power supply. In this laboratory a voltmeter and ammeter were respectively used to measure the voltage across and the current through a given circuit. 
 

However, there are other sources of error that may have contributed to the 1,0 % error.The resistors, themselves, are probably the biggest source of error. The last color band indicates the tolerance except when there is a temperature coefficient band. Precision resistors have the tolerance printed as a number. Temperature is the second major source of error. Then having errors in multimeter, and might have cold sloder connections, thermocouples, moisture, electrolytes and gremlins.

 

SUGGESTIONS AND COMMENTS
Because the procedure of the experiment is not difficult and the concept is easy enough, the manual and steps could be understood easily. In other words; the lab manual was functional. Another good point was that, in first part of the experiment in questions step, there are 2 questions and in second part there are 2 questions too and  these questions answer the whole conclusion part of our report. That’s very simple and perfect.

REFERENCES
·         [online document] Retrieved from  http://physics.bu.edu/py106/notes/Circuits.html
[online document] Retrieved from  http://www.oocities.org/wdupre11066/Introduction/samplelabreport.h

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