OHM'S Law - General Physics Laboratory II - Lecture Notes | PHY 222, Study notes of Physics

Download OHM'S Law - General Physics Laboratory II - Lecture Notes | PHY 222 and more Study notes Physics in PDF only on Docsity! IV. OHM’S LAW==================================== f05.01 INTRODUCTION The electric field, with which you are familiar from the previous experiments, usually causes a flow of charges, or simply an electric current. Ohm’s Law says that a value of electric current in a piece of conductor depends linearly on the electric potential applied to it: I = V R The constant R is called electrical resistance and it depends on the material forming the conductive element, its size and shape, but it does not depend on the applied potential. Unlike fundamental Coulomb’s and Gauss’ Laws, which are always true, Ohm’s Law is not universally true. For example, for semi-conducting elements like diodes Ohm’s Law is not obeyed at all. Elements which obey Ohm’s Law are called resistors. Different resistors can be combined into a circuit. The flow of current through each element of the circuit is completely charac- terized by the total applied voltage and the resistance of the individual resistors. We will learn the rules for calculating the effective resistance of a composite circuit. PURPOSE • Study of elements that obey and violate Ohm’s Law. • Verification of the rules for resistors arranged in parallel or in series. OHM’S LAW IV-1 PRE-LAB ASSIGNMENTS A. Readings: Ohm’s Law states that the current I through a piece of conductor depends linearly on the potential difference V between the two ends of the conductor. For objects that obey Ohm’s Law we may define a constant quantity - electrical resistance R - which is simply the ratio of the potential difference and the current: R = V I (1) We measure resistance in units of: [Ω] ≡ [Ohm] = [V olt]/[Ampere]. For elements that don’t obey Ohm’s Law the resistance is not a constant quantity, thus it does not play a useful rule. Elements which obey Ohm’s Law are called resistors. What happens if we combine two such resistors together in series? R1 R2 f f V IB£ £ ££ £ ££ £ ££ £ ££ £ ££B BB B BB B BB B BB B B £ ££ £ ££ £ ££ £ ££ £ ££B BB B BB B BB B BB B B The current through them has to be the same, even if the resistors are different, because the current cannot be lost along its path. The total voltage drop across the two resistors will be the sum of the voltage drops across each of them: V = V1 + V2 = I1R1 + I2R2 = I(R1 + R2) From (1): V = IReff therefore, we have the series rule for the effective resistance Reff : Reff = R1 + R2, (2) which can be easily generalized to an arbitrary number of resistors Reff = R1 + R2 + R3 + R4 + . . . (3) IV-2 OHM’S LAW REPORT SHEET IV–1 Date Name Instructor PRE-LAB EXERCISES Exercise 1. At home, if you plug two lamps in the same double-outlet, are you connecting these lamps in series or in parallel? Explain. Exercise 2. Assume you have two 100Ω resistors, but need 50Ω resistor. Is there a way to connect the 100Ω resistors to get 50Ω? Exercise 3. Calculate effective resistance of three resistors connected as shown. R =100 Ω R =200 R =50 1 2 3 Ω Ω OHM’S LAW IV-5 blank IV-6 OHM’S LAW LABORATORY ASSIGNMENTS Materials Needed: • Resistors: 2Ω, 220Ω, two 100Ω • Diode (Experiment B) • Rheostat • 4.5V Battery • Dual Channel Amplifier with voltage probes • ULI computer interface box • Voltmeter (for apparatus test only) • Cables Experiment A: Ohm’s Law The Task: To observe linear dependence of I on V for a resistor and to measure its resistance, R. Procedures A-1. To verify Ohm’s Law we need to measure the potential difference V across the resistor and the current I flowing through it for a wide range of V . The circuit to perform these measurements is shown here: ε V I R To vary V we need to use variable source of potential difference ε This can be achieved by connecting a battery to a rheostat as shown in figure below. Rheostat is a device OHM’S LAW IV-7 A-5. Now try to measure actual resistance of 2Ω resistor. You are likely to run into problems with the method we have been using so far, since the potential difference across the resistor is so small that it becomes comparable to the measurement inaccuracies and we cannot measure it very well. One possible solution is to move the slider on the rheostat only at the end that produces the highest potential difference (and current) across the resistor. Even better way is to perform a fit of a straight line to the I vs. V graph. Select this graph by clicking on it. Go to “Analyze” menu and select “Linear Fit”. This should superimpose the fitted line on your graph and a box with the fit results. The fitted functions is “y = m x + b” where in our case y = I, x = V and the slope m = 1/R. Thus, you can determine resistance by inverting m. Since we graph the current in units of milliampers (mA), to obtain resistance in units of Ohms you should calculate R = 1000/m. IV-10 OHM’S LAW REPORT SHEET IV–2 Date Name Instructor Partner(s) A. V (V) I (mA) Current vs Potential (for 220Ω resistor) Nominal resistance Measured resistance A-3 220Ω A-4 100Ω A-5 2Ω OHM’S LAW IV-11 blank IV-12 OHM’S LAW REPORT SHEET IV–3 Date Name Instructor Partner(s) V (V) I (mA) Current vs. PotentialB-1. 0 1 2 3 4 5 6 7 8 9 10 Time (s) V/I (Ω) Resistance vs. TimeB-1. B-1 Does the diode fulfill Ohm’s Law? Ex- plain. Does the diode have a constant resis- tance? B-2. Maximal absolute value of current for the reverse connections of the diode |I|max = What can you say about value of the current through the diode in this case as compared to the maximal value ob- tained in B-1? OHM’S LAW IV-15 blank IV-16 OHM’S LAW Experiment C-F: Resistors Connected in Series and in Parallel The Task: To verify the rules for effective resistance of resistors connected in series and in parallel. Procedures If for any of configurations of resitors you are going to study, the effective resistance becomes small, use the fit method described in A-5 rather than averaging of the V/I mea- surements. C. Connect in series 220Ω and 100Ω resistors instead of the diode. The voltage probe 1 should be connected across both resistors. Collect the data for varying applied poten- tial. From V/I vs. time graph calculate average effective resitance and note it down in Report Sheet IV–4. Calculate the expected effective resitance from the rule for the resistors connected in series. Use the measured rather than nominal values of the re- sitance for each resistor (from IV–2). Report your calculation in Report Sheet IV–4. How does the measured effective resistance compare with the calculated one? D. Now connect the same resitors in parallel. Collect the data for varying applied potential and determine average effective resitance. Calculate the expected effective resistance and report both in Report Sheet IV–4. E. Add 2Ω resistor in parallel to the other resistors. Before making any measurements or calculations make a rough guess of the effective resistance of the three resistors connected in parallel. Now make the measurement and the calculation (Report Sheet IV–4). F. Connect 2Ω resistor in series with 220Ω and 100Ω resistors connected in parallel. Make a rough guess of the effective resistance of the system of resistors. Now make the measurement and the calculation (Report Sheet IV–4). OHM’S LAW IV-17