Lab 5: Ohm’s Law
Ohm’s Law – PHY202 Introduction This virtual experiment has two parts. The purpose of the first part of this experiment is to verify Ohm’s Law. The purpose of the second part of this experiment is to explore the equivalent resistance of combinations of resistors connected in series and in parallel. Theory In metals and some other materials (in particular, commercially manufactured resistors), one finds experimentally that the voltage drop, V, across the material is directly proportional to the current I, flowing through the material (provided the temperature remains relatively constant): VαI which is referred to as Ohm’s Law. It is convenient to define a proportionality constant between voltage and current, called the resistance R (unit: Ohm [Ω] = V/A), such that: V = IR Eq. (1) A resistor generally means a device that obeys Ohm’s Law (many devices do not) and has a resistance R. Two (or more) resistors can be connected in series (as in Figure 1), or in parallel (as in Figure 2). Resistors could also be connected in a series/parallel combination (as in Figure 3). An equivalent resistor is a single resistor that could replace a more complex resistor combination and produce the same total current when the same total voltage is applied. For a series combination of resistors, the resistances are additive. If there are two resistors in series: Req = R1 + R2 Eq. (2) where Req is the equivalent resistance. For a parallel case, the resistances add as reciprocals. If there are two resistors in parallel: 1/Req = 1/R1 + 1/R2 Eq. (3) A more complex circuit, like the one shown in Figure 3, can be handled by noticing that R1 and R2 are in parallel and can be reduced to an equivalent resistance using Equation 3. That equivalent resistance is then in series with R3 and can be treated using Equation 2 to find the equivalent resistance of the entire series/parallel circuit. Figure 1: Series Figure 2: Parallel Figure 3: Series/Parallel Procedure Open the PhET simulation Circuit Construction Kit DC and select Lab: https://phet.colorado.edu/sims/html/circuit-construction-kit-dc/latest/circuitconstruction-kit-dc_en.html 1. Ohm’s Law a) Using the PhET simulation, build a single loop circuit consisting of a battery, a 10 W resistor and the wires necessary to close the circuit. Keep the wire resistivity as tiny and the battery resistance as zero. b) Use a voltmeter to measure the voltage across the ends of the resistor and an ammeter to measure the current that flows through the resistor. c) Note that if you click on the battery or the resistor you can change their values. d) Record the values of the voltage across the resistor terminals and current flowing through the resistor, starting with a voltage of 10 V and increasing, in steps of 10 V, until you reach 100 V. e) Create a voltage vs current graph. Make sure you are using appropriate IS units. Analysis of part 1: Ohm’s Law Use a linear function (y = mx + b) to fit the data in the graph. a) Does your data support Ohm’s Law? Explain fully, don’t state just yes or no. b) Calculate the value of the resistance from the fitting parameter ‘m’? c) Calculate the % Difference Error between the fitting value and the value used in the simulation: % Difference Error = 100*([Fitting Value]-[Simulation Value]) / [Simulation Value]. Include a copy of the table and the graph with the fitting in your report as well as the answers to the analysis questions. 2. Equivalent Resistance Circuit Diagrams a) For each of the three circuit diagrams shown above, use the PhET simulation to build the corresponding loop circuit consisting of a battery, the appropriate resistors and the wires necessary to close the circuit (connect the ends of the battery to points A and B, respectively). Keep the wire resistivity as tiny and the battery resistance as zero. b) Select 10 V for the voltage of the battery. Use a voltmeter to measure the voltage across the resistor combination (from point A to point B) and an ammeter to measure the current that flows through the resistor combination (through points A and B). Use these values to calculate the equivalent resistance for each of the three resistor combinations. c) Calculate analytically the equivalent resistance for each of the three resistor combinations. d) Enter the pertinent data in the table shown below using appropriate units. Case Voltage Current Simulation Resistance Analytical Resistance Series Parallel Series/ Parallel a) How well do the equivalent resistances and analytically calculated, compare? Include a copy of the table in your report as well as the answers to the analysis questions.
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