Ohm s Law. The purpose of this lab is to learn through experiment to distinguish between ohmic and nonohmic

Transcription

1 Johnson 1 Cameron Johnson Jun Li Physics 223 February 17, 2013 Ohm s Law Abstract The purpose of this lab is to learn through experiment to distinguish between ohmic and nonohmic materials, understand current-voltage relationships, and use Ohm s Law to calculate the values of current and voltage using our gathered information. Introduction A relationship exists in electricity travelling through a material between voltage V and current I when the two are associated with a resistance R. This relationship is described by Ohm s Law which states that in many cases, I is proportional to V and the R of the material through which the electricity is travelling is defined as the ratio between the two. Materials that behave in this manner are said to obey Ohm s Law and are called Ohmic. Ohmic materials have a constant or linear resistance over a wide range of voltages. Materials that do not obey Ohm s law are called Non-Ohmic. Non-Ohmic materials have a non-linear resistance when voltage is changed. The behavior of Ohmic materials can be related to the behavior of water travelling through a pipe. With a constant pressure (voltage in electricity), the rate at which the water moves through the pipe (current in electricity) can be hindered by the radius and length of the pipe, as well as any obstructions (resistance in electricity). At constant pressure, as the obstructions in the pipe increase, the flow rate of the water decreases. If the pressure is increased, and the obstructions are held constant, the flow rate will increase as long as the pipe is large enough to hold all the water at any given moment. If too much water is in the pipe and the pressure continues to

2 Johnson 2 increase, the pipe itself could begin to hinder the flow and if the pressure becomes high enough the pipe could burst or begin to leak. These relationships in the water in a pipe scenario are analogous to the relationships in the electricity in a wire scenario. The pipe bursting with too much water pressure would be analogous to a resister frying when too much voltage is applied. In this lab, we will set up a circuit with variable resisters and apply various voltages to observe the effects of the relationship between current, voltage, and resistance. We will take measurements and then use Ohm s Law to calculate the unknown. Theory Definitions & Formulas: Ohm s Law: relates the voltage (V) and current (I) associated with a resistance (R): R = V I V = II Ohm (Ω): the unit of resistance with units Volt/Ampere (V/A). Point Charge (q): if the electric field is due to a single point charge, then it can be described by: E = kk r 2 Ohmic: a material that has constant resistance that is said to obey Ohm s law. Non-Ohmic: a material with a non-linear voltage-current relationship that is said not to obey Ohm s law. Rheostat (R h ): a variable resistor that allows the voltage across the resistance R s to be varied. (This combination is sometimes called a voltage divider because the rheostat divides the voltage across itself and R s ). Decade Resistance Box (R s ) Any component in a circuit that does not generate or supply a voltage acts as a resistance in the circuit. Applying Ohm s Law to the portion of the circuit with R s only gives: V s = IR s Voltage drop across R h : V h = IR h Applying Ohm s Law to the entire circuit: V t = V h + V s = IR h + IR s = I(R h + R s )

3 Johnson 3 Example of the relationship between Resistance, Current, and Voltage: N.d. Graphic Apr < Experiment To begin this experiment, we first obtained an ammeter, voltmeter, multimeter, decade resistance box (R s ), rheostat (R h ), a resistor of unknown resistance, a power supply, switch, and connecting wire. We then connected the electrical components in series in the following order: power source to switch, switch to decade resistance box, decade resistance box to ammeter, ammeter to rheostat. We then connected the multimeter set for voltage in parallel to the circuit so that one lead

4 Johnson 4 was connected just before the decade resistance box and the other was connected just after the ammeter. For the first part of the experiment, we set the terminal voltage of the power source to a constant DC voltage of 6.00 V and set the decade box to a constant resistance of 50Ω. We then set the rheostat at the maximum resistance, turned the power supply on and closed the circuit with the switch. We measured the voltage from the multimeter and the current from the ammeter and recorded the results in our data tables. We then set the rheostat to four consecutively lower resistances and recorded the voltage and current at each resistance. We then set the decade resistance box to 30Ω and again set the rheostat at maximum resistance. We again measured and recorded initial voltage and current readings and then did the same for four consecutively lower rheostat resistances. We then repeated this procedure except this time we replaced the decade resistance box with a resistor of unknown resistance. For the second part of the lab, we put the decade resistance box back into the circuit so that the circuit was set up as it was originally. We set the decade box to 90Ω and set the rheostat to its maximum resistance. We then closed the circuit with the switch and adjusted the rheostat until the voltage read at approximately 4 V. We recorded the current in our data tables. We then lowered the resistance of the decade resistance box by 10Ω four more consecutive times. Each time, we adjusted the rheostat so that the voltage was again approximately 4 V. We recorded the current and resistance of the decade resistor box each time and entered it into our data tables. Data/Calculations (Refer to attached sheets)

5 Johnson 5 Questions pp. 249 Questions #1, 2 1. What is the definition of electrical resistance? The resistance of a material is defined as the ratio of applied voltage and the resulting current. 2. What is ohmic resistance? Are all resistances ohmic in nature? Ohmic resistance is when a material shows constant resistance over a wide range of applied voltages. Not all materials in nature are ohmic, these are called non-ohmic materials. pp Questions #1 1. If the switch were kept closed during the procedures and the circuit components heated up, how would this affect the measurements. If this scenario occurred, the resulting increase in temperature would increase the resistance in the circuit causing the current to go down.

6 Johnson 6 Discussion In this experiment, we were able to observe how varying the resistance on a circuit effects the current when the terminal voltage is held constant and likewise when the voltage in a part of the circuit is held constant. In each case, we found that as the resistance increases, the current decreases. We were also able to calculate the resistance of a resistor of unknown resistance by applying Ohm s law to the data collected when the resistor was placed in the circuit. When we compared our results to the theoretical calculated results, we found that in each case, our error was not too far off. Sources of error could include inaccurate readings and not fully reliable interconnects.