PHYS272_Lab2

Physics for Scientists and Engineers - Lab 2 PreLab
 Assignment: Read chapter 6 of the book Experimentation: An Introduction to Measurement Theory and Experiment Design, paying particular attention to sections 6-5 and 6-7. Perform the calculations described below. This assignment is due at the start of the laboratory period. These concepts will be used to complete the lab.

Questions:
 1. There are 3 equations for calculating the power dissipated by a resistor: //P = IV//, //P =// I 2 //R//, and //P =// V 2 ///R//. Suppose you measure the resistance of a resistor, the current flowing through it and the voltage across it and get measurements of R = 1001 ± 1 Ω, I = 2.02 ± .01 mA and V = 2.015 ± .001 V. Use each of the 3 equations to calculate power. Also calculate the uncertainty in each of your 3 calculations. For the uncertainty calculations use the fact that, if //y=f//(//x// 1, //x// 2 ) then math \Delta y = \sqrt{(\partial f / \partial x_1)^2 \Delta x_1^2 + (\partial f / \partial x_2)^2 \Delta x_2^2}. math Do the 3 uncertainty intervals overlap? 2. You perform an experiment where you measure the current flowing through a resistor and the voltage across it. You obtain the following table of data for current and voltage values. Comparison with Ohm's Law //V = RI// shows that if you were to let the voltage measurements be a set of //y// i values and the current measurements be a set of //x// i values, you could perform a linear regression to find a slope value equivalent to the resistance //R//. a) Use equation 6-3 from your textbook to calculate a value for the slope and equation 6-4 to calculate the y-intercept. b) Use equations 6-1, 6-5 and 6-6 to calculate the uncertainty in the slope. This calculation assumes that all of the uncertainty in the y (voltage) measurements can be estimated by the departure of the data points from a straight line and uses that discrepancy to estimate the uncertainty in the slope. c) If the resistance of the resistor is found to be 1000 ± 5Ω, does your calculated uncertainty overlap this interval? d) Since we actually know the uncertainty in the voltage measurements, we can use it for //S// y in equation 6-6. Redo the calculation for uncertainty in the slope using the uncertainty in voltage for //S// y.
 * ~ I ||~ V ||
 * 2.02 ± .01 mA || 2.02 ± .01 V ||
 * 4.01 || 3.99 ||
 * 6.00 || 5.98 ||
 * 8.02 || 7.99 ||
 * 10.01 || 9.96 ||

=Physics for Scientists and Engineers - Lab 2 =

Objectives:

 * To study the relation between current and voltage in direct current circuits.
 * To make direct measurements of resistance, current and voltage.
 * To make calculations of power dissipation.

Equipment:

 * Two Digital multimeters
 * DC power supply, 0-15 V
 * 6 Selected Resistors, such as 100 Ω, 300 Ω, 1000 Ω, 2200 Ω, 3300 Ω, 4700 Ω
 * Circuit boards, circuit board leads
 * Graphical Analysis software

Physical Principles:
 The current in a circuit, measured in Ampere, is defined to be the rate charge passes a point in a circuit. math I= \frac{dq}{dt} math The voltage at a point, measured in volts, is the work per unit charge required to move a charge from some arbitrary reference point to that point. Voltage is sometimes called the electromotive force, it “pushes” the current through circuits. When a voltage is applied across a conductor the resulting current is directly proportional to the applied voltage. The proportionality constant is defined by math R=\frac{V}{I} math where R is called the resistance and is measured in ohms (Ω).

When current flows in a circuit, the voltage (work/charge) times the current, (charge/time) is the power (work/time) supplied to the material. The electrical power P measured in watts is math P = IV = I^2R = \frac{V^2}{R} math

math R = NN \times 10^M math where NN is called the two digit nominal value and M is the multiplier exponent. The values of these parameters are given in the table below. For example, a resistor with bands [Brown, Black, Red] would be R = 10 x 10 2 Ω = 1000 Ω. Some resistors also have a fourth band, which represents precision according to the following table.
 * Resistor Color Code** The resistance of a resistor is indicated by the color bands on it according to the formula below,
 * ~ Color ||~ Value ||
 * Black ||> 0 ||
 * Brown ||> 1 ||
 * Red ||> 2 ||
 * Orange ||> 3 ||
 * Yellow ||> 4 ||
 * Green ||> 5 ||
 * Blue ||> 6 ||
 * Violet ||> 7 ||
 * Gray ||> 8 ||
 * White ||> 9 ||
 * Gold ||> -1 ||
 * Silver ||> -2 ||
 * ~ Color ||~ Precision ||
 * No band ||> 20% ||
 * Silver ||> 10% ||
 * Gold ||> 5% ||
 * Brown ||> 2% ||
 * Black ||> 1% ||

Procedure:
  **Learning the resistor color code** Measure the resistance of six resistors with different values and complete table 1 in your journal. In the first four columns record the colors of the resistor bands. Compare the readings from the digital multimeter (click here for multimeter reading uncertainties) with the values obtained from the color code. Calculate the uncertainty in the resistance by multiplying the indicated resistance by the precision. Then find the difference between the resistance from the color code and your measurement. In the last column indicate whether the difference fell within the uncertainty predicted by the 4th band.  **Table 1**  //**Create the Following Table:**//

Resistance || % Precision || Uncertainty || Measured Resistance || Difference || Is Difference < Uncertainty? (Y/N) ||
 * || Color 1 || Color 2 || Color 3 || Color 4 || Indicated
 * Resistor 1 ||  ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
 * Resistor 2 ||  ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
 * Resistor 3 ||  ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
 * Resistor 4 ||  ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
 * Resistor 5 ||  ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
 * Resistor 6 ||  ||   ||   ||   ||   ||   ||   ||   ||   ||   ||

<span style="color: #333333; font-family: 'Apple Color Emoji','Segoe UI Emoji',NotoColorEmoji,'Segoe UI Symbol','Android Emoji',EmojiSymbols; font-size: 16px;">‼️ ** Safety Warning **<span style="font-family: 'Apple Color Emoji','Segoe UI Emoji',NotoColorEmoji,'Segoe UI Symbol','Android Emoji',EmojiSymbols; font-size: 16px;">‼️ <span style="color: #333333; display: block; font-family: Arial,sans-serif; font-size: 14px;"> Resistors can get hot and burn up! Make sure both knobs on your power supply are turned all of the way down before turning it on then increase both current and voltage slowly. Turn off your power supply if you smell smoke. Be careful touching resistors if they have just had current running through them <span style="color: #333333; display: block; font-family: Arial,sans-serif; font-size: 14px;"> Connect a resistor of approximately 1000 Ω and two digital multimeters as shown in figures 1 and 2. The black probe should be in the common receptacle and the red lead should be in the receptacle bordered by the red region, labeled V for voltage measurements and A for current measurements, be sure to include the uncertainties in these measurements. Take a series of voltage measurements when the current is set to about 0.002, 0.004, 0.006, 0.008, 0.010 A, again be sure to include the uncertainties in these measurements. Record a table of voltage and current measurements in your journal. Calculate the power dissipated by the resistor for each of your measurements, including the uncertainty in each value using the same technique as in prelab question 1 for P=IV. Calculate the resistance (slope) using equation 6-3 just as you did for prelab question 2 and the uncertainty in the slope using 6-1, 6-5 and 6-6. Now plot a graph of voltage versus current. Make sure you include error bars in your graph. Have the graphing program calculate a linear fit. Does the computer's estimation of the slope agree with your calculation? Does the reported RMSE correspond to anything you calculated? Does the uncertainty you calculated give a resistance interval that overlaps with that measured? Recalculate the uncertainty in the slope using the uncertainty in the voltage measurements for //S// y in equation 6-6. How does this interval compare? <span style="color: #333333; display: block; font-family: Arial,sans-serif; font-size: 14px;"> For the same circuit hold the voltage constant at about 10 volts, and measure the current and voltage for six different resistors. Record a table of current, power, resistance, and 1/resistance (use the actual measured values for each resistor as determined in part 1). Make sure that you calculate the uncertainty for both power and 1/resistance. Plot a graph of current versus the reciprocal of resistance and compare the slope to V. Use equation 6-6 to find the uncertainty in the slope with //S// y = the uncertainty in your y (current) measurements. Comment on whether your slope interval includes 10V. Plot a second graph of power versus the reciprocal of resistance and compare the slope to V 2, once again using 6-6 to calculate slope uncertainty. Make sure that error bars are included in your plots. <span style="color: #333333; display: block; font-family: Arial,sans-serif; font-size: 14px;"> For the same circuit, hold the current constant, and measure the current and voltage for six different resistors. Record a table of voltage, power, and resistance (use the actual measured values for each resistor as determined in part 1). Plot a graph of Voltage versus resistance and compare the slope to I, calculating the slope uncertainty with 6-6. Plot a second graph of Power versus resistance and compare the slope to I 2, using the slope uncertainty. Include error bars in all plots.
 * Ohm's Law in the case of a constant resistor**
 * Ohm’s Law in the case of constant voltage**
 * Ohm’s Law in the case of constant current**