

resistors in series and in parallel 


The objective of the study is to understand and differentiate the resistance, voltage, and the current relations in circuits in series and in parallel Series circuits 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:
resistance of resistors in series : R = R1 + R2 + R3 + ...Rn
A series circuit is shown in the diagram above. The current flows through each resistor in turn. If the values of the three resistors are:
R1 = 8 ohms R2 = 8 ohms R3 = 4 ohms the total Resistance is 20 which is derived from 8 + 8 + 4; the sum of the 3 resistors.
With a 10 V battery, by V = I R the total current in the circuit is:
I = V / R = 10 / 20 = 0.5 A. The current through each resistor would be 0.5 A.
In Series, the current is the same.
Parallel circuits
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 recombining 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 +...+1/Rn
A parallel circuit is shown in the diagram above. In this case the current supplied by the battery splits up, and the amount going through each resistor depends on the resistance. If the values of the three resistors are:
R1 = 8 ohms R2 = 8 ohms R3 = 4 ohms the total Resistance is derived by using the formula above. Substituting the values in the formula, we have: 1/8+1/8 + ¼ = ½. Which means that the resistance is equal to 2 ohms.
Given a 10 V battery, by V = I R (ohms law) the total current in the circuit is: I = V / R = 10 / 2 = 5 A.
The individual currents can also be found using I = V / R. The voltage across each resistor is 10 V, so:
I1 = 10 / 8 = 1.25 A
I2 = 10 / 8 = 1.25 A
I3=10 / 4 = 2.5 A
In parallel circuits, the voltage is the same.
V1 = V2 = V3 =? = Vn
From the Reference: http://buphy.bu.edu/py106/notes/Circuits.html
III. DIAGRAM/MATERIALS
? battery
? voltmeter
? ammeter
? 3 resistance boxes
? wires
SETUP 1 SERIES
SETUP 2 PARALLEL
SETUP 3 PARALLEL AND SERIES
IV. PROCEDURE
The power source, wire, and the 3 resistance boxes are arranged in a way that it follows the setup above. In all the setups the current is determined through the ammeter, the voltage through the ammeter, the 1st 3 resistances should be set at 10,20,30 ohms. Record the current, voltage, and the resistances in their respective tables. Calculate the missing values (refer to the formula below V) and compute for the percentage difference.
V. DATA
Table 1 ? Resistors in Series
Resistance R (Ohms) Voltage V ( Volts ) Current I (Amp) Computed R V/I (Ohms)
R1 10 ? V1 0.2 I1 0.02 V1/I1 10
R2 20 ? V2 0.4 I2 0.02 V2/I2 20
R3 30 ? V3 0.6 I3 0.02 V3/I3 30
R4 65 ? V4 1.3 I4 0.02 V4/I4 65
R4* 60 ? V4* 1.2 %R4 8% %V 8%
R4*= R1 + R2 + R3 V4* = V1 + V2 + V3
R4 = V4/I4
Table II Resistors in Parallel
Resistance R (Ohms) Voltage V (volts) Current I (amp) Computed R
R1 10? V1 1.25 volts I1 0.07 V1/I1 17.9 ?
R2 20? V2 1.25 volts I2 0.04 V2/I2 31.25?
R3 30? V3 1.25 volts I3 0.03 V3/I3 41.67?
R4 8.92? V4 1.25 volts I4 0.14 V4/I4 8.92?
R4* 5.45 ? %R 48% I4* 0.14 %I 0%
R4* computed from 1/R1 + 1/R2 + 1/R3
I4* = I1 + I2 + I3
Table III Resistors in Parallel and Series
Resistance R (Ohms) Voltage V (volts) Current I (amp) Computed R
R1 10? V1 1.1 volts I1 0.08 V1/I1 13.75 ?
R2 20? V2 1.3 volts I2 0.05 V2/I2 26 ?
R3 30? V3 1.3 volts I3 0.04 V3/I3 32.5 ?
R4 23? V4 2.4 volts I4 0.08 V4/I4 30 ?
R4* 22? R* 2.4 I4* 0.12 %I 40%
R4 = R1 + 1/ ((1/R2)+ (1/R3))
V4*= V1 + V2
VI. SAMPLE COMPUTATION
SERIES:
R4*= R1 + R2 + R3
= 10 + 20 + 30
= 60?
V4* = V1 + V2 + V3
= 0.2 + 0.4 + 0.6
= 1.2 volts
PARALLEL
R4* computed from 1/R1 + 1/R2 + 1/R3
R4* = 1/10 + 1/20 + 1/30
= 5.45 ?
I4* = I1 + I2 + I3
= 0.07 + 0.04 + 0.03 amperes
SERIES AND PARALLEL
R4 = R1 + 1/ ((1/R2)+ (1/R3))
V4*= V1 + V2
R4 = 10 + 1/ ((1/20)+1/30))
= 23 ?
V4*=1.1+1.3
= 2.4 volts
Percentage Difference
%V= / 1.31.2 / = 8%
/(65+60)/2/
%R= / 6560 / = 8%
/(1.3+1.2)/2/
VII. ANALYSIS
Based on the data that we have gotten from the experiment, we have proven that the current in series is equal and the voltage in parallel circuits are the same.
I have also noticed that adding resistors in series has increased its total resistance while connecting additional resistors in parallel has decreased the total resistance. This explains that the total resistance of the resistors in series is greater than the individual resistances while on the contrary; the total resistance of a parallel group is always less than the individual resistances.
The percentage difference of the experiment is due to the malfunctioning of the materials while we were conducting the experiment.
VIII. CONCLUSION
In conclusion, I can say that connection is in series when electricity flows uniformly from one resistor to the next. In series, the current is equal and the total voltage is derived by adding their individual voltages. The total resistance of a series connection is also derived by adding their individual resistances.
However, when the connection is parallel the total current is the result of the sum of the individual currents while the voltage is equal. The reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances.
The total resistance of the resistors in series is greater than the individual resistances while on the other hand; the total resistance of a parallel group is always less than the individual resistances.













