dc circuits

1. Kaitlyn Greiner
Formal Lab Report:
Title of Experiment: Simple dc Circuits
Date Performed: July 16th, 2014
Lab Partners: Erin Phlegar and Stephen Few
Physics 102L, Section: 02
Professor Teklu
Abstract:
In this lab, my objective was to understand the relationships between resistance, potential
difference, and current in a simple circuit. To accomplish this, we built a series and parallel
circuit each containing three resistors. We measured the current and potential differences across
the resistors on each circuit. I learned that, in a series circuit, the current remains the same
throughout the circuit and the potential difference varies across each resistor. In a parallel circuit,
the current varies across each resistor and the potential difference remains the same throughout
the circuit.

2. Introduction:
In this experiment, we are investigating the relationships between resistance, potential difference,
and current in a simple circuit. We are going to learn how to build simple circuits. We are going
to build both a series and parallel circuit. Before obtaining our measurements, we expect to find
that the current will remain the same and the potential difference values will vary across the
resistors of the series circuit. We expect to find that the opposite is true for the parallel circuit.
We think that the values for current across each resistor will vary from each other and that the
potential difference value will be the same across the circuit.
Description of Apparatus:
To build our series circuit, we connected a power supply to three different resistors using clips
and wires. The resistors were lined up all next to each other. A voltmeter was used to obtain our
measurements. We placed the two leads of the voltmeter on each side of each resistor and the
power supply to obtain our voltage values and current values. Our series circuit looked like the
one in the sketch below:
To build our parallel circuit, we connected a power supply to three different resistors in parallel
using wires and clips. The three resistors were more vertically stacked than in a line. A voltmeter
was used to obtain our measurements for this circuit as well. Two leads of the voltmeter were
placed on each side of each resistor and the power supply to obtain voltage and current values.
Our parallel circuit looked like the one in the sketch below:

3. Procedure:
We first built our series circuit. We set up a series circuit with three resistors to determine
how resistors affect current and voltage. We measured the current and voltage of each resistor.
To measure the voltage, we placed the two leads of the voltmeter on either side of each resistor
and across the power supply and recorded the value for each. We then added the voltages at each
resistor together to get the measured voltage value. We measured current in same way but we
switched to amps instead of voltage when measuring. We recorded this value as our measured
current. We then calculated the current and voltage for the series circuit. We used four volts as
our set voltage value and added the three resistances together for our equivalent resistance value.
We plugged these values into this equation, I= ΔV/Req, to calculate our current. Lastly, we
calculated an overall percent error for our measured and calculated current and voltage for the
series circuit.
Next we built our parallel circuit. We set up a parallel circuit with three resistors to
determine how resistors affect current and voltage. We measured the current and voltage of each
resistor. To measure the voltage, we placed the two leads of the voltmeter on either side of each
resistor and across the power supply and recorded the value for each. We recorded this value as
our measured voltage. We measured current in same way but we switched to amps instead of
voltage when measuring. We then added the current at each resistor together and recorded this
value as our measured current. We then calculated the current and voltage for the series circuit.
We used four volts as our set voltage value and added the inverse of the three resistances
together to find the equivalent resistance value (1/Req=1/R1 +1/R2 + 1/R3). We plugged these
values into this equation, I= ΔV/Req, to calculate our current. Lastly, we calculated an overall
percent error for our measured and calculated current and voltage for the parallel circuit.
Results:
Series Circuit:
Calculations:
R1=1kΩ
R2=2.2kΩ
R3=3.3kΩ
R1+R2+R3=6.5kΩ  6500Ω
1+2.2+3.3=6.5

4. Req=6500Ω
Voltage: 4V
I= ΔV/Req
I=4/6500
I=6.15x10^-4 A
Current is always the same number throughout a series circuit.
Calculated Current: 6.15x10^-4 A
MeasuredCurrent: 6.10x10^-4 A
I1=I2=I3=6.10x10^-4 A
% Error: (calculated-measured)/calculated x100
(((6.15x10^-4)-(6.10x10^-4))/(6.15x10^-4)) x100 = .813%
% Error for Current: .813%
Voltage is not the same number throughout a series circuit.
Calculated Voltage: 4 V
MeasuredVoltage=3.993 V
V1=.603
V2=1.363
V3=2.027
V1+V2+V3=V
.603+1.363+2.027=3.993 V
% Error for Voltage: .175%
((4-3.993)/4) x100= .175%
Data Tables:
I1 (A) I2 (A) I3 (A) I (A) Overall
Measured 6.10x10^-4 A 6.10x10^-4 A 6.10x10^-4 A 6.10x10^-4 A
Calculated 6.15x10^-4 A 6.15x10^-4 A 6.15x10^-4 A 6.15x10^-4 A
Experimental
Error %
.813%

5. V1 (V) V2 (V) V3 (V) V (V) Overall
Measured .603 1.363 2.027 3.993
Calculated 4 V 4 V 4 V 4 V
Experimental
Error %
.175%
Parallel Circuit:
Calculations:
Voltage: 4V
I= ΔV/Req
1/Req=1/R1 +1/R2 + 1/R3
Current is not the same number throughout a parallel circuit.
I1= V1/R1
I1=4/1000
I1=.004
I2=V2/R2
I2=4/2200
I2=.0018
I3=V3/R3
I3=4/3300
I3=.0012
I1+I2+I3= I
.004+.0018+.0012=.007
Calculated Current: .007
MeasuredCurrent: .00702
I1=.00120
I2=.00179
I3=.00403
.00120+.00179+.00403=.00702
% Error for Current: .286%
((.007-.00702)/.007) x100= .286%
Voltage is the same number throughout a parallel circuit.
Calculated Voltage: 4V

6. MeasuredVoltage: 3.98V
V1=V2=V3=3.98V
% Error for Voltage: .5%
((4-3.98)/4) x100= .5%
Data Tables:
I1 (A) I2 (A) I3 (A) I (A) Overall
Measured .00120 .00179 .00403 .00702
Calculated .004 .0018 .0012 .007
Experimental
Error %
.286%
V1 (V) V2 (V) V3 (V) V (V) Overall
Measured 3.98V 3.98V 3.98V 3.98V
Calculated 4V 4V 4V 4V
Experimental
Error %
.5%
Conclusions:
In the series circuit, the current across each resistor is the same number throughout the
circuit (I1=I2=I3). Any charge that flows through one resistor also flows through the other. The
measured voltage across each resistor varied. V1, V2, and V3 were different values. The sum of
these potential differences is equal to the total potential difference across the circuit. The
equivalent resistance of a series circuit is the sum of each resistance. If one part of this circuit
failed, none of the other parts would work either. The low percent error for current shows that
this formula, I= ΔV/Req, is accurate. Both percent errors were very low. This means that very
little mistake was made during the experiment for the series circuit.
In the parallel circuit, the current across each resistor was not the same number
throughout the circuit. The values for I1, I2, and I3 were different. The current that enters a point
must be equal to the total current leaving the point. Therefore, the overall current is the sum of
each individual current. The voltage across each resistor was the same number throughout the
circuit (V1=V2=V3). The values are the same because each resistor is connected directly across
the battery terminals. The equivalent resistance of a parallel circuit is the sum of the inverses of
each resistance (1/Req=1/R1 +1/R2 + 1/R3). The percent errors for current and voltage are very
low. This means that very little mistake was made during the experiment for the parallel circuit.