Write you name on the white label on the component box in your kit
Lab #1: Imperfections in Equipment practice with parallel and series circuits, and Ohm’s law Measure the internal resistance of a battery Measure the input impedance of the oscilloscope Measure the output impedance of the signal generator Theme: model the real by an ideal in series with a resistor.
Basic electrical terms Make sure you have a solid conceptual understanding of the following terms, their relations, and their differences voltage electric field current electric potential resistance
Current/Voltage Current Current: amount of charge that passes a point on the wire each second (Ampere = Coulomb/second) Determined by number of charges and by their speed Voltage Potential energy/charge (normalized potential energy) Voltage across something. Current through something.
Basic Electrical Concepts Conductors Terminal velocity depends on voltage, the geometry of the materials, and the properties of the material Resistivity Ohmic materials: Use a battery or some other emf to set a voltage across an object. Chemical reaction in the battery allows rearrangement so as to maintain an (approximately) constant voltage difference between the two terminals.
Resistor code Use this to choose the resistance. But never use this value as the resistance. Always measure it. This applies as well to the resisitor box. Never use the nominal values. Always measure.
Kirchhoff’s Rules From course work, remember how to use Kirchhoff’s rules to calculate voltage and currents in circuits? If not, see lab writeup. In going round a closed loop, the total change in potential must be zero Charge is conserved so that at any junction the current flowing into the junction is equal to the current flowing out of the junction Applying these rules to enough junctions and loops generally leads to enough equations to solve for the number of unknown currents and voltages.
Effective Resistance When calculating currents and voltages in a circuit, you can replace these combinations by an “effective resistance” without altering the current through and voltage across these “elements” Sometimes you can use these shortcuts instead.
Circuits When using these rules, you probably neglected to take into account the fact that the instruments you use to measure the circuit can themselves alter the performance of the circuit. We will study this in the lab, see how big the effect is, and from that get an idea of when this needs to be taken into account when comparing results to predictions.
Internal Resistance of a Battery Imagine a simple circuit consisting of a battery and a resistor. ε If you varied the resistance R and plotted V versus I, what would you get? A horizonal line, independent of R
Simple circuit A more realistic model If I plotted V vs I, what would I get now? I get a straight (not flat) line. What does the slope represent? What does the intercept represent? ε r
An even more realistic model Will get r A and r V from meter manual and estimate effect on estimate of r and ε
Input/Output Impedences A function generator, like a battery, is a voltage source. An oscilloscope, like a multimeter, is a measuring instrument. We will measure the “internal resistance” of each of these devices.
Using the multimeter Discuss how to use it for current and voltage measurements. Point out the 400 mA and 10 A terminals for the ammeter and discuss their purpose. Be sure it is set to ‘DC’ not ‘AC’
Never measure the value of a resistor when it is in a circuit
Estimating Errors: Review Systematic errors : sources of error that have the same size effect on every measurement that is made (or a correlated effect) a ruler that was not manufactured correctly a consistently delayed reaction when using a stop watch your inability to perfectly estimate the size of a stray magnetic field from your computer that leaks into your experimental area Random errors : sources of error whose effect varies with each measurement precision of your measuring device when using a stop watch, a reaction time that sometimes anticipates the event, some times is in retard of the event.
Multi-meter systematic errors Will assume that the systematic error due to the factor calibration is in the form
Systematic Errors and fits Last week, we learned how to propagate errors in measured quantities to errors in quantities calculated from them via a simple algebraic formula (both random and systematic are handled the same way). how to calculate the uncertainty on the fit slope and intercept from a linear fit due to random errors in the x y variables This week we’ll learn how to calculate the uncertainty on the fit slope and intercept from a linear fit due to systematic errors in the x-y variables.
Error on slope and intercept due to statistical error Note error on intercept scales with 1/root(N)
Fitting and systematic errors Suppose you are measuring V using a meter that has infinite accuracy and that has no random errors, but that always reports a voltage that is always off by 0.25V? Adding more measurement points does not reduce the error. Previous formula can not work for systematic errors
Systematic Error in Slope How can slope be changed? If voltage is always off by a scale factor, or if current is always off by a scale factor, slope is off by the same factor. The error in the offset (b) does not cause an error in the slope at all.
Systematic Error in Intercept What if the voltage is always off by a fixed, constant amount? (see “Propagation of Systematic Errors” on the class web site, for a more complete, rigorous derivation of this result.)
Random and Systematic errors first, fit to a straight line using only random errors get the error on the fit m and b due to random errors from the spreadsheet calculate the errors on m and b due to systematic errors as shown on previous 2 slides take the error on m due to random errors and the error on m due to systematic errors and add them in quadrature ditto for b
Fitting and Systematic Errors If you don’t understand this (how to calculate the systematic error on slope/intercept and then combine with the statistical error), don’t leave the room today until you do! It’s important for this and future labs!
linearizing This semester, we will often do a variable transformation in order to get a linear dependence that we can easily fit.
Linearizing When we transform variables, we also need to recalculate the errors. In this lab:
Rounding Uncertainties If your digital voltmeter says 3.02 V, the real measurement could be between 3.015 and 3.025V with equal probability. What is the uncertainty? -> want +- 1 sigma to include 68% of the measurements. least significant bit (lsb)
Sqrt(12) When you have an LSB, what is the random error? Imagine a step with width centered at zero. Remember:
Notes on lab check that probes are not set on x10 check that ammeter is set on DC, not AC Never use the nominal value of a resistor. Always measure the resistance using an ohm meter. Always remove the resistor from the circuit before measuring its resistance (why?) All numbers should have units and be carefully labeled. Some of the resistors have values that drift with temperature. It is important to measure V&I simultaneously. If you measure one, wait a minute, then measure the other, you’ll get a bad result. There will be a random error from your ability to read the 2 meters at the same time. How will you estimate this random error? (Drift is biggest when using smallest resistor. Why?) Be careful with grounds when measuring the output impedance of the signal generator.
Be Careful on This Step! Start with the voltage set to 0 on the variable-voltage power supply, and slowly increase, keeping current I < 400 mA I Voltage knob … otherwise the fuse is blown in the ammeter Power Supply