Ohm’s Law Lab Objective To experimentally verify Ohm’s law using circuits, as well as to learn to construct and diagram simple circuits. Theory The universe naturally wishes to exist in the lowest state of energy possible. Naturally, this extends to charge in a wire as well; it wishes to neutralize itself and therefore charge will flow from high potential to low potential. This results in a flow of electric charges, known as current. How much current goes through a circuit is dependent upon the resistance of the circuit, measured in Ohms. Therefore, Ohm’s Law states that: π = πΌπ Where V is voltage, I is current, and R is resistance. Notable in this context are circuit components known as resistors, which contain significantly larger resistance values than the passive values of other equipment, such as wires. When making circuits, there are 2 distinct states for components: series and parallel. When components are “in series,” they are directly in line with each other, meaning the output from one goes directly into another. However, when components are “in parallel,” the components both lie on distinctive split paths, through which the current can choose either path in order to reach the other side; in essence, each component has its own path which is split off from the main path and which reconnects with the other splits paths at some point. Of course, these can be mixed and matched. For instance, a resistor in a parallel configuration can have another resistor added onto its path before it reconnects with the other parallel paths, meaning that those two are in series with each other and in parallel with all other paths collectively. When drawing circuits, each distinct component has its own symbol which connects with the wire of the circuit. Due to Ohm’s Law being perfectly linear, any relationship between the separate components therein should be a straight line which in some way represents another component. For instance, in a voltage vs. current graph, the resistance would become the slope of said straight line as per the typical slope equation: π¦ = ππ₯ + π Notable in this regard though, are instances where a given component changes in ways not described by Ohm’s Law. For instance, a light bulb has a resistance which changes as the wire within the bulb’s temperature changes. Therefore, Ohm’s Law no longer holds as you cannot accurately find the resistance based on the voltage and current; you must derive a new equation which includes the added temperature dependency. Apparatus -DC Power Supply -Rheostat -Alligator Clips -Fixed Resistor -Two Switches -At least 2 Lamps -Voltmeter -Ammeter Procedure 1. We start by ensuring the power supply is off and at the lowest voltage possible. Then, we connect the power supply in series with one lamp and a switch. We then proceed to turn on the power supply and increase the voltage somewhat to ensure the circuit works as intended, before once more turning it off. Lastly, we draw a diagram to represent this circuit 2. Create a circuit with two lamps in series with a single switch. We then turn the power supply on and increase the voltage to ensure the circuit is working as intended, before turning the power supply down to 0 V and turning it off. Once we have determined that the circuit works as intended, we draw the circuit diagram. 3. Create a circuit with one lamp in parallel with one switch. We then turn the power supply on and increase the voltage to ensure the circuit is working as intended, before turning the power supply down to 0 V and turning it off. Once we have determined that the circuit works as intended, we draw the circuit diagram. 4. Create a circuit with two lamps in parallel with each other and in series with one switch. We then turn the power supply on and increase the voltage to ensure the circuit is working as intended, before turning the power supply down to 0 V and turning it off. Once we have determined that the circuit works as intended, we draw the circuit diagram. 5. Create a circuit with two lamps in parallel with each other and where the switch turns off a single lamp. We then turn the power supply on and increase the voltage to ensure the circuit is working as intended, before turning the power supply down to 0 V and turning it off. Once we have determined that the circuit works as intended, we draw the circuit diagram. 6. Create a circuit with two lamps in series and where the switch turns off a single lamp. We then turn the power supply on and increase the voltage to ensure the circuit is working as intended, before turning the power supply down to 0 V and turning it off. Once we have determined that the circuit works as intended, we draw the circuit diagram. 7. Create a circuit with two lamps, each with a switch that turns them individually off. We then turn the power supply on and increase the voltage to ensure the circuit is working as intended, before turning the power supply down to 0 V and turning it off. Once we have determined that the circuit works as intended, we draw the circuit diagram. 8. Turn off your power supply and turn your rheostat to the highest setting. Designate one multimeter to the DC voltage setting and one to the current setting. 9. Build a circuit wherein your DC power supply, switch, ammeter, fixed resistor, and rheostat are all in series with one another. Connect your voltmeter in such a manner that it lies in parallel to only the fixed resistor. 10. Ensure that the switch is open before turning on the power supply. 11. Close your switch and increase your power supply to 10 V. Record both the voltmeter and ammeter readings alongside the setting on the rheostat. 12. Decrease the setting on your rheostat and record the new resistance value. Take a measurement of the current and voltage through your multimeters. 13. Repeat step 12 until you have a total of 8 data points, all at varying rheostat settings. 14. Replace the unknown resistor with a lamp and repeat steps 12-13. 15. Create a graph of voltage vs. current, and find a line of best fit. The slope of this line should be equal to the resistance of your fixed resistor. 16. Repeat step 15 for the data from your lamp. 17. Graph both data sets in order to create a graph with resistance as the slope. Data Unknown Resistor Rheostat (β¦) Voltage (V) Current (mA) 176.3 3.448 34.78 155.8 3.72 37.69 134.0 4.07 41.20 116.2 4.43 44.96 84.0 5.15 52.22 53.9 6.19 62.82 99.4 4.68 47.50 5.0 8.88 91.0 Rheostat (β¦) Voltage (V) Current (mA) 37.3 1.22 222.5 27.4 1.93 283.5 20.1 2.47 324.5 15.7 3.35 380.4 12.4 3.23 395.5 Unknown Bulb Results Simple Circuit -Contains a single lamp and switch, when the switch is pressed the lamp turns on Lamp and Switch in Parallel -Contains a lamp and a switch in parallel with one another, when the switch is pressed the lamp nearly or completely turns off. Two Lamps in Series, 1 Switch in Parallel -Contains 2 lamps in series, one of which has a switch in parallel with it. When the switch is pressed, the lamp it is in parallel with turns off. Two Lamps in Parallel, 1 Switch in Series -Contains two lamps in parallel with one another. A single lamp is in series with a switch. Only the lamp not in series with the switch is on until the switch is pressed, at which point both lamps will be on. Two Lamps in Parallel and in Series with 1 Switch -Contains two lamps which are in parallel with one another. The circuit also contains a switch which is in series with both lamps. The lamps do not turn on until the switch is pressed, at which point both lamps will turn on. 2 Lamps and 1 Switch in Series -Contains 2 lamps and a switch all in series with one another. The lamps are initially off until the switch is pressed, at which point both lamps will turn on. The first lamp in series is brighter than the second one. Two Lamp/Switches in Parallel -Contains 2 lamp-switch pairs which are in parallel with one another. When either switch is pressed, the lamp it corresponds to turns on. Both lamps can be turned on simultaneously by pressing both switches at once. Current vs. Voltage Graph (Unknown Resistor): Current vs. Voltage Graph (Bulb): Experimental Resistance Values: Unknown Resistor: 96.8 β¦ Bulb: 12.5 β¦ Discussion Overall I would say this lab is successful in demonstrating Ohm’s Law and teaching about circuits. Each circuit acted exactly as it was expected to within the context of the rules given to us, and our measurements for the unknown resistor demonstrated a very strong correlation with the rule that V=IR through our graph, with an r-squared value of 1.000. In said graph the “b” value from y=mx+b must be 0 as b represents an initial value, and due to Ohm’s Law you cannot have voltage exist in a circuit without current and vice versa, meaning that when the current is 0, voltage must also be 0. When two bulbs are wired in series they share the same current, however when two bulbs are wired in parallel they have different currents but share the same voltage. The heat energy in a bulb not dissipated through light most likely dissipates through the physical connections between the wire and the bulb itself, such as the glass or any metal portions the heating coil inside might be near. We did see some nonlinearity in the light bulb measurements, however it is difficult to make any kind of notable observation about the nature of this nonlinearity due to the imprecision of the bulb measurements (possibly due to equipment issues). However, this nonlinearity is still likely due to the bulb heating up to such a point that the change in temperature drastically changes the resistivity of the material which makes up the coil, which results in a negative feedback loop stopping any more current from passing through than is enough to maintain a specific temperature. Two major sources of error in this lab are the aged equipment and the inherently inaccurate nature of light bulbs in this context. -TrueThe equipment, particularly the rheostat, had a notable problem wherein certain settings seemed to not act as intended, and had resistance values which varied wildly even when the rheostat remained still. Upon closer inspection the rheostat seemed to have either dirt, grime, or rust on this portion of the bar, which may have resulted in the rheostat not acting as intended while in that specific setting. Other than this, the light bulbs themselves seemed old and particularly fragile, and did not act entirely consistently even between themselves, with some not shining as brightly when exposed to the same conditions as others. -The inherently inaccurate nature of light bulbs refers to the expectation that the light bulb will not follow the rules set in place by Ohm’s Law at all times. As a result, although we can see that it does in fact not follow the rule as expected, it is still difficult to accurately describe the situation, as the testing conditions were not ideal to thoroughly test it (particularly the condition of the equipment, which seemed somewhat fragile, meaning it would’ve been risky to increase the temperature of the bulb significantly).
