DC Circuits Lab
Purpose
The goal of these experiments is for the student to develop an understanding of direct current circuits consisting of batteries and resistors (or other resistances). Series and parallel connections will be explored as well as the resistance properties of batteries, meters, and lamps.
Procedure
All circuits will be constructed on the Vernier Circuit Board. The board is powered by two D-cells, in series provide 3 volts to terminals 1 (+) and 35 (-) when switch SW1 is in the “3V” position. It is good practice to leave this switch off except when actually making observations and measurements of the circuit (the “External” position is equivalent to OFF unless an external power supply is connected to terminals J1 and J2). Jumper cables with alligator clips are used to connect the various parts of the circuit. Note that the circuit elements on the board have binding posts to which two alligator clips may easily be connected – one atop the other.
Parts A, B, C – Series Resistors, Parallel Resistors, Kirchoff’s Laws
Calculate the theoretical currents and voltages for the circuit shown based on the ratings of the batteries and resistors. Show work in the space provided and enter the results in the table. Note that currents are shown in a certain direction in the diagram – if the conventional positive current is in the opposite direction enter it as a negative in the table.
Construct the circuit and measure the currents and voltages using digital multimeters. The measured values should be fairly close to the values based on ratings – if not check the connections and settings of the meter and also your calculations. Do not expect perfect results – ratings for electronic equipment are typically nominal values.
Part D – Batteries, Meters, and Lamps
In this experiment the real properties of electrical elements will be explored. The internal resistance of a battery and of a meter, and the varying resistance of a lamp, will be investigated by varying the current and measuring the voltage.
Construct a simple series circuit incorporating the 3 V battery, an ammeter, a “resistance”, and a bulb. This circuit should be a single loop such that each element carries the same current as shown on the ammeter. Use a voltmeter to determine the voltage across: the battery, the ammeter, and the bulb. Vary the “resistance” so that different amounts of current flow in the circuit. The “resistance” can be a single resistor or a combination of resistors to achieve a resistance value not available on the board with a single resistor. And the “resistance” can be a conductor such that it is essentially zero ohms.
Analyses
1. Produce a graph of voltage vs. current using data from Part D. Show all three devices on one graph using different symbols and/or colors and include a key or legend.
2. Use a calculator or computer to determine the line of best fit for the battery and the meter and an appropriate curve for the lamp. Plot the lines and curve and include the equation on the graph.
Questions
1. (a) Use the data from Part A to determine the actual resistance of each resistor based on the measurements of voltage and current. (b) Calculate the percent difference from the rated values. Show all work.
2. (a) Use the data from Part B to determine the actual resistance of each resistor based on the measurements of voltage and current. (b) Calculate the percent difference from the rated values. Show all work.
3. Consider voltage vs. current for the battery. (a) Use Kirchoff’s Laws and knowledge of voltage, current, and resistance to derive an expression for a battery’s terminal voltage, Vt, as a function of its emf, ε, its internal resistance, r, and the current, I, that passes through it. (b) Compare this function to the curve fit for the battery from Part D and identify and state the values of the emf and internal resistance based on the coefficients of the equation.
4. Consider voltage vs. current for the ammeter. (a) Based on the results of the curve fit, what is the resistance of the ammeter? (b) Does it appear to be an ohmic device? Explain.
5. Consider voltage vs. current for the lamp. (a) Does it appear to be an ohmic device? Explain. (b) As the power increases, does the resistance of the lamp increase or decrease? Explain.
6. Discuss how the results verify or refute the concepts of Ohm’s Law, Kirchoff’s Laws, equivalent resistance, etc. and explain how so with specific references to tables, graphs, calculations, etc.
7. Discuss error.
Part A – Series Resistors
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I2 I1 |
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Based on Ratings: |
Based on Measurements: |
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I1 |
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I2 |
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V0 |
3.00 V |
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V1 |
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V2 |
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Req |
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Note: Req represents the combined equivalent resistance of the two resistors.
Show calculations for the values based on the ratings:
Part B – Parallel Resistors
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Based on Ratings: |
Based on Measurements: |
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I0 |
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I1 |
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I2 |
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V0 |
3.00 V |
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V1 |
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V2 |
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Req |
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Note: Req represents the combined equivalent resistance of the two resistors.
Show calculations for the values based on the ratings:
Part C – Kirchoff’s Laws
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Based on Ratings: |
Based on Measurements: |
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I1 |
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I2 |
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I3 |
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V0 |
3.00 V |
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V1 |
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V2 |
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V3 |
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V4 |
6.00 V |
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Note: The currents are each drawn arbitrarily pointing to the right. If the actual (conventional) current is leftward this should be indicated as a negative value in the table.
Show calculations for the values based on the ratings:
Part D – Batteries, Lamps, Meters, etc.
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Current (mA) |
Potential Difference (V) |
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Battery |
Ammeter |
Lamp |
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0.000 |
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0.000 |
0.000 |
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Draw a schematic diagram showing all circuit elements including placement of meters. Note: show the voltmeter in three locations illustrating the various voltage measurements.