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PHYS2070 INSTRUMENTATION FOR SCIENTISTS AND ENGINEERS – LABORATORY OENG1208 Circuits - Measurement of Voltage, Current and Resistance Student ID Name Max Mark Mark Preliminary Exercise 10 Part A: Characteristics of a Single Resistor I-V plot 4 Questions 6 Part B: Series Combinations of Resistance I-V plot 4 Questions 6 Part C: Resistors in Parallel I-V plot 4 Questions 6 Total 40 DC Circuits - Measurement of Voltage, Current and Resistance Aim: (a)To measure circuit voltages and currents and apply Ohm’s Law to calculate circuit resistances. (b)To measure resistance of linear (Ohmic) resistors and investigate their behaviour in series and parallel configurations. Original Apparatus: Digital Voltmeter, Clamp Ammeter, Power Supply, Plug panel, a selection of test Resistors. Replaced with: Partsim circuit simulator Theory: See Appendix at end of laboratory notes and relevant theory in lecture notes. A note from Jim... This laboratory was intended to be performed as a hands-on exercise with real components, power supplies etc. Due to the necessity for online learning, I have replaced the lab with a circuit simulation. This is to be performed individually using a freely accessible circuit simulater that runs over the internet and through any internet browser. I have included detail from the real lab-based circuit where suitable to highlight differences between reality and simulation. You will also find pictures of the real circuit for reference. Preliminary Exercise: 1. Calculate the equivalent resistance of the combinations of resistors shown in figure 1(a), (b) and (c) below for the case of: R1 = 120 , R2 = 200 , R3 = 300 . Enter your results in the spaces below. ___ ___ Figure 1: (a) Series combination of resistors (b) Parallel combination of resistors (c) Combination of series/parallel. ___ 2. What is the potential difference between the arrows (outputs) of the following two circuits? ____ Volts ____ Volts Experiment Part A:Characteristics of a single resistor. (i)The circuit required for Part A is shown in figure 2 (with R = 220 ) as a schematic. Figure 2Part A circuit schematic. The 220 Ω resistor (R) is the ‘test’ resistor (ie. resistor being measured). Figure 3(a):Equipment set up for Part A: The multimeter is set to DC voltage input. The red plug is a wire link to complete the circuit. The clamp ammeter is on the right. We are going to set the circuit up virtually using a circuit simulator. Using your browser (Firefox or Chrome), go to partsim.com and click “try it now”. You will see something like this... Figure 4. Initial screen in Partsim. You now need to add components. These are all located under “GENERIC PARTS” on the left-hand side of the screen. Click GENERIC PARTS to see this pane (Fig. 5). Figure 5. GENERIC PARTS in Partsim First select Sources and voltage source. Click and drag this to the schematic area. Next select Ports/GND and add two of these to the circuit area. From “Test Equipment” select Ammeter and place one on the circuit area. Finally, you need the resistor - this you’ll find in “Passives”. Once the resistor is on the circuit area, you can click on it to change its default value to 220 Ω (220 Ohms). You should see something like this now (Fig. 6) Figure 6. Partsim components required for PART A circuit. Next, the components can be linked up by dragging wires that appear when you hover the cursor over the terminals (ends) of the components. Using this feature, set the circuit up as in Fig. 7 Figure 7. PART A circuit completed. Now the circuit is ready for the simulation. Click “Run” in the top menu bar. You will then see the window shown in Fig. 8 below. Tick the box for DC sweep only. Set the start voltage as 0 V and the stop voltage as 10 V with a step of 1 V. Click run on this window and the simulation will begin. It takes only a few seconds typically and the results will display automatically. Figure 8. The “run” window for the circuit simulation. The output from the simulation is a current-as-a-function-of-voltage (or ‘I-V’) plot. Copy this plot into this document overleaf: I-V plot here Figure 9. I-V characteristic from the Partsim PART A circuit. Questions on Figure 9: Explain whether the resistor in the circuit obeys Ohms law. Answer: What is the gradient of the plot equal to? Answer: And what are the SI units for this gradient? Answer: When a voltage of 10.0 V is applied across the resistor, what is the power transformed by the resistor? Answer: Part B.Series Combinations of Resistors Figure 10. Circuit for Part B – Series Combinations of Resistors (i)Now connect the circuit in Partsim as in figure 10. There is now a combination of a 220 resistor in series with a 100 resistor. (ii)Set the DC sweep parameters as before (0 - 10 V with 1 V step). Copy the resulting I-V plot into this document here: Figure 10. I-V characteristic from the Partsim PART B circuit. Questions on Figure 10. Show that the slope of the plot is equal to the reciprocal of the sum of the two resistors. Answer: Has the power transformed in the 220 Ohm resistor increased or decreased as a result of adding the 100 Ohm resistor in series? Answer: Part C.Resistors in Parallel Figure 11:Circuit for Part C Resistors in Parallel. (i) For Part C, set up the circuit configuration as shown in Figure 11. Two resistors (220 and 470 ) are now in parallel. (ii)Set the DC sweep parameters as before (0 - 10 V with 1 V step). Copy the resulting I-V plot into this document here: Figure 12. I-V characteristic from the Partsim PART C circuit. Questions on Figure 12. Has the power transformed in the 220 Ohm resistor increased or decreased as a result of adding the 470 Ohm resistor in parallel? Answer: Finally, if a very large resistor is in parallel with a small resistor, what is the maximum possible value for the effective resistance? Give reasons for your answer. Answer: Appendix: Important Electrical Quantities Electric Charge. The fundamental quantity in electricity is electric charge. This is represented by the symbol Q or q. Charge is measured in coulomb (C). The smallest unit of charge is the charge on the electron (e) = -1.6 x 10-19 C. The electronic charge is very small, it takes 1/e = 6.24 × 1018 electrons to equal 1 C. Electric Potential Difference (Voltage) is a measure of the amount of electrical energy per unit charge. Unit:volt (V)(1 V = 1 J/C) or U = QV It takes 1 J of energy to move 1 C of charge through a potential difference of 1 V. We need to consider two quantities (both with the unit of V): Electromotive Force (emf) is a measure of the energy supplied per unit charge by the source (eg. battery or power supply). Potential Difference (pd) is a measure of the energy per unit charge used by the circuit component(s). In any closed loop in an electric circuit conservation of energy applies. The total emf (measure of energy input) is equal to the total of all pd’s (energy dissipated in circuit components (eg. resistors, lamps, etc.). Electric Current When electric charges move in a circuit there is an electric current. Current is defined as the rate of flow of charge. Current is measured in ampere (amp) Symbol A( 1 A = 1 C/s ) If there is a current of 1 A flowing through a conductor, then 1 C of charge will flow in 1 s. Electrical Resistance When charges collide with atoms in a conductor they lose energy which is transferred to the material. This causes heating of the conductor as the energy lost by the moving charges is converted to heat. A continual energy input is required to maintain an electric current and the conductor opposes the flow of charge. This opposition to flow is referred to as resistance. For many conductors the current through the conductor is proportional to the potential difference across its ends. These are referred to as linear or ohmic conductors and they obey Ohm’s Law. Ohm’s Law For linear conductors: and the constant of proportionality is known as the resistance (R) of the conductor. The unit of resistance is the ohm (). Resistance can be calculated by measuring the voltage across the resistor (voltmeter) and the current through the resistor (ammeter) and using (1 = 1 V/A). Alternatively the current in a circuit can be calculated by measuring the voltage across a known resistor and using Ohm’s Law to calculate the current. If a conventional ammeter were used to measure current it would require that the circuit be opened and an ammeter inserted in series with the other components before reconnecting the circuit. In these experiments a clamp ammeter will be used which measures the current in a wire without the need to open the circuit. For a linear or ohmic conductor a graph of V versus I for a resistor will be a straight line with a slope of R. Note that the characteristic curve of an electronic component is usually a plot of current as a function of voltage, in which case the slope will be . Circuit Symbols Battery or The long line is the positive (+) terminal. Resistor Note that an arrow drawn through a resistor indicates a variable resistor. Similarly an arrow through a battery symbol represents a variable voltage source. Potentiometer or Voltage Divider Voltmeter V A voltmeter must always be connected across (in parallel) the ends of the component to be measured. Ammeter A An ammeter must always be connected in series with the component in order to measure the current through it. Ground or Earth The ground represents a zero potential reference point in the circuit. Figure A1:Some common circuit symbols. Combinations of resistors Resistors may be connected in series, parallel or a combination of the two as shown in figure A2 (a), (b), (c) below. Figure A2:(a) Series combination of resistors (b) Parallel combination of resistors (c) Combination of series/parallel. 1.Series combination of resistors. In the circuit shown in figure A3, resistors R1 and R2 are connected in series. Obviously the current is the same in both resistors since the electrons flowing through R2 must flow through R1.