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# Physics

In: Science

Submitted By rerosa15
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Lab #3: Controlling Currents
09/18/13

Objective-

The first objective in this lab is to determine how a light bulb behaves in different circuit arrangements. The second objective investigates how the voltage across the light bulb varies with the amount of current through it. Finally, the last objective is to explore how the length of a wire affects resistance.

Procedure- Activity 1
A) Measure the voltage across an open-circuit cell by connecting the positive terminal of the voltmeter to the positive terminal of the call and the negative terminal of the voltmeter to the negative terminal.

The voltage across cell #1 is 1.462 V. The voltage across cell #2 is 1.455 V.

B) Measure the voltage across two cells connected in a series.

The voltage across two cells is 2.9 V. C) Connect the circuit as shown in the diagram below. Insert two D-cells into the circuit.

D) What is the effect of rotating the knob on the device that is identified as a “Potentiometer”?

Rotating the potentiometer adjusted the brightness of the light bulb.

Activity 2
A) Set the multimeter to the 200/400 mA range. Connect the circuit as the same in activity one with the ammeter in the circuit. Set the second multimeter to the VDC scale and connect its leads across the bulb.

B) Read the current that is flowing through the bulb. Measure the voltage across the bulb. Record both values in the data table below.

C) Turn the knob of the potentiometer and increase the current about 20 mA at a time. Measure and record the voltage and current each time.

D) Remove the bulb from your circuit and replace it with a 10 Ω resistor. Measure the voltage across the resistor for different values of the current flowing through the system. Continue this process until you have gotten enough data to establish the relationship of voltage versus current.

Activity 3
A) Compute the ratio of the voltage and current to compare these quantities for two different cases. Keep the appropriate number of significant figures.

B) Use the data from activity 1 to make a scatter plot in MS Excel.

C) Should the point (0,0) be included?

D) Is it appropriate to add a linear trend line?

E) What does the chart tell you about the way the current vary with voltage for the bulb? For the resistor? Record observation.

Activity 4
A) Set up apparatus as described. Measure the voltage across the wire. The current in the circuit can be read from the display. Use the equation R=V/I to calculate R. Record the data corresponding to each length of wire.

B) Make a graph of the resistance versus length. Is the relationship linear? Does the best-fit line pass through the origin? What does this tell you about the relationship between R and the length l?

C) Repeat step A for the rest of the diameters.

D) Make a graph of R versus diameter D. Is the relationship linear? If not try a graph of R versus 1/D and 1/D2. Which attempt gives a linear relationship? What does this tell you about how R is related to the wire cross-section area?

Precautions-

Double check your wiring and circuit connections and use the diagrams provided. Always check to see that the power switch is OFF before plugging into the outlet. Also, turn instrument or equipment OFF before unplugging from the outlet. Be cognizant that the ground is grounded to Earth. Make sure the multi-meter is set to proper mode for the measurement being made and never put in current mode for any other measurement. Check for all the connections of the circuit and scope connections before powering the circuit, to avoid shorting which may lead to electrical shocks or damage of equipment.

Analysis and Results
Data-
Activity 2
BULB RESISTOR
VOLTAGE (V) CURRENT (A) RATIO: VOLTAGE/CURRENT VOLTAGE (V) CURRENT (A) RATIO: VOLTAGE/CURRENT
0.149 0.0766 1.95 0.633 0.0617 10.3
0.136 0.0865 1.57 0.726 0.0716 10.1
0.213 0.0966 2.20 0.828 0.0816 10.1
0.217 0.1063 2.04 0.929 0.0916 10.1
0.375 0.1166 3.22 1.029 0.1015 10.14
0.486 0.1268 3.83 1.132 0.1116 10.14
0.673 0.1364 4.93 1.231 0.1216 10.12
0.761 0.1468 5.18 1.363 0.1346 10.13
0.940 0.1568 5.99
1.055 0.1665 6.336

Activity 4
Length (m) Voltage (V) Current (A) Resistance (ohm)
0.24 0.0335 1.00 0.0335
0.20 0.0280 1.00 0.0280
0.16 0.0223 1.00 0.0223
0.12 0.0167 1.00 0.0167
0.08 0.0110 1.00 0.0110
0.04 0.0050 1.00 0.0050

Diameter (m) Voltage (V) Current (A) Resistance (ohm)
0.00130 0.0137 1.00 0.0137
0.00100 0.0214 1.00 0.0214
0.00081 0.0335 1.00 0.0335
0.00051 0.0874 1.00 0.0874

1/D (1/m) R (Ω)
1960.78 0.0874
1234.57 0.0335
1000.00 0.0214
769.23 0.0137

1/D2 (1/m2) R (Ω)
2.601E-07 0.0874
6.561E-07 0.0335
0.000001 0.0214
0.00000169 0.0137

Calculations-

Activity 2
The equation R=V/I was used in the table to calculate the ratio.

Activity 3
% Error=((Theoretical-Experimental)/(Theoretical))×100%

Using this equation, our percent error was 5.3% Activity 4
The equation R=V/I was used in the table to calculate the ratio.

(i)
Slope=ρ/〖πr〗^2 ρ=71 ×〖10〗^(-9 ) Ωm r=0.00081/2m slope=0.1378Ω

ρ=mA m=0.1378Ω A=5.15×〖10〗^(-7) m ρ=7.10×〖10〗^(-8) Ωm

% Error= .012%

(ii)
Slope=4Lρ/π ρ=71 ×〖10〗^(-9 ) Ωm L=0.24m slope=2.14×〖10〗^(-8) Ω

ρ=m(π/4L) slope=2.14×〖10〗^(-8) Ω L=0.24m ρ=7.00×〖10〗^(-8) Ωm

% Error= 1.36%

Graphs-

Activity 2

Activity 4

Questions-

Activity 3

C) Should the point (0,0) be included?

The point (0,0) should not be included.

D) Is it appropriate to add a linear trend line?

It would only be appropriate to add a linear trend line to the graph of the resistor. An ohmic resistor is one where the value of the resistor does not change over varying voltages and currents. The light bulb is a non-ohmic resistor.

E) What does the chart tell you about the way the current vary with voltage for the bulb? For the resistor? Record observation. The chart tells us that the brighter the bulb, the bigger the current flowing through it and the lesser amount of resistance, same for the resistor. Current and voltage are directly proportional.

Activity 4

B) Make a graph of the resistance versus length. Is the relationship linear? Does the best-fit line pass through the origin? What does this tell you about the relationship between R and the length l? The relationship is linear, and the best-fit line passes through the origin. This shows that R is directly proportional to L. D) Which attempt gives a linear relationship? What does this tell you about how R is related to the wire cross-section area?

1/D2 should have given a linear relationship but the data did not show this. R is related to the cross sectional area by the slope of the graph which is given with the equation: slope=ρ 4/〖πD〗^2 . R is proportional to 1/D2.

Conclusions-

In activity 2 and 3 of this experiment a standard three terminal potentiometer was used in conjunction with two multimeters to measure the voltage and current moving through a light bulb and a 10-Ω resistor. Upon graphing the bulb showed a parabolic trend proving that the light bulb itself is a non-ohmic and unknown resistor. The 10-Ω resistor proved linear and to be an ohmic resistor. The use of the potentiometer proved that current is directly proportional to the potential difference or voltage across two points and inversely proportional to the resistance between them. Resistance is the physical meaning of the slope of the graph of voltage versus current. Both sections prove Ohm’s law and that Ohm’s law applies to only ohmic material. In activity 4, the relationship of the length of a wire and its resistance was explored. It was proven that resistance is proportional to the length of the wire and inversely proportional to the cross-sectional area. A wire has more resistance if it long and thin and less resistance if it shorter and has a longer diameter. In the longer thin wire there is much less room for electrons to flow freely thus resisting the electrical current.

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