X x Physics: Electricity WCLN.ca\" Name: Are you clever enough to determine unknown circuit components by analyzing voltages and currents from other, more accessible areas? What does it mean to measure a parameter \"indirectly\"? Electricians, technicians, and engineers are often required to determine the values of unknown resistors (or other components) through indirectly measuring other areas of the circuit where taking voltage and current readings is more convenient. This procedure is referred to as indirect measurement and requires a solid understanding of Kirchhoff's Laws. Using a graphical approach will often help \"average out\" the data. But you need to be clever... \\ ; . 2021-Oct01-BOL Page 10of9 Physics: Electricity WCLN.ca Open the Phet simulation below entitled Circuit Construction Kit: DC. https://phet.colorado.edu/sims/html/circuit-construction-kit-dc/latest/circuit-construction-kit-dc_en.html The clout ecoment to edit Grout Construction KI-DC 5 Build the circuit below by dragging the components onto the screen. R. RZ RX MV Ix assume unknown Voltage 5.0 V 5.00 V 50.0 0 75.0 0 100.0 0 0.05 A 0 22A 2021-Oct01-BOL Page 2 of 9Physics: Electricity WCLN.ca Procedure: 1. The values of Ri and R2 are known, and you will ASSUME the value of R. is your unknown. Set the values of Ri and R2 below by clicking on each resistor (adjust the slider to the values below) and choosing to show Values. The last resistor will be set to 100 2. This is our unknown and you will check at the end to confirm your answer. R1 = 75 2 R2 = 50 2 Rx = 100 2 (again, assume that this is our "unknown") 2. Place the two ammeters such that you are able to measure the total current in the circuit Ir as well as the current through the unknown resistor Ix as shown in the circuit above. Part 1 Background Knowledge: Let's organize all of the physics that is going on by using Kirchhoff's Laws to determine the relationships between V, I, and R for this particular circuit 3. Let's start with Kirchhoff's Current Law. . State this law in your own words. The Current entering a node in a circuit must equal the total current leaving the same . Write an equation that relates Ir to I1, 12, and Ix. Kirchhoff's Current Law equation for this circuit: IT = Ix + I1 + Iz C. Prove that your above equation is true by setting your total voltage to 25 V and, using the Non-Contact Ammeter, found on your simulation, recording the values of Ir to I1, Iz, and Ix. For Vr= 25V (record the currents below) Ir= 1.1 A, I1= 0.5 A , 12 = 0.3 A, Ix = 2.5 A Use the currents above to test your answer to (b) above. Show all work below. 1. 1 = 2.5 + 0.5 + 0.3 2021-Oct01-BOL Page 3 of 9Physics: Electricity WCLN.ca 4. Now let's look at Kirchhoff's Voltage Law. a. State this law in your own words. The sum of electrical potential differences around any closed path in a network is always equal b. Grab a voltmeter and measure the voltages directly across RI, SRi, R2, and Rx, as well as across the battery, Vo. Discuss how Vo, V1, V2, and Vx relate to each other. Record values below using Vo = 25V. For Vr= 25V (record the currents below) Vo = 25 V , V1= 25 V, V2 = 25 V, Vx= 25 V c. Discuss how your above values agree with the law as stated in (a) above. The voltage remains the same . 5. What type of circuit is this (how are the resistors are connected)? Series/Parallel (circle) 6. How could you determine the total resistance, Ro, of this circuit? Describe two ways below: Formula for total resistance, Ro, of this circuit using the variables Ro, R1, R2, and Rx Ro = Rit Rz + RX Ro = Rit R2 + RX Formula for total resistance using Ohm's Law, V = IR (be specific with the correct subscripts - ie. V1 = IRI would represent the voltage across R1 precisely) VI = IIR. V2 = Iz Rz V x = TyRy V = (0.5 ) ( 2.5 ) = 1.25 = 0.30 * 25 = 0.23 X25 Vz = 7.5 Vx = 5.8 2021-Oct Page 4 of 9X WCLN.ca Data: Adjust the battery's voltage by clicking on it and setting the slider. Startata 5V. Gradually increase the voltage in regular increments such that you are able to make measurements for It and Iy, Record your values in the data table below. Voltage (V) Ir(A) L. () 5 0.0 O .05 10 Q.50 0.\\% 15 | 0.3 D.1% 20 | 0.9% 0.4 25 ' |\\ 0.1% 30 \\.4 6.3%5 35 | \\.5 0.%3 40 | L] o0-4Y5 45 \\ [:9 0-4% 50 I 2.1 0-55 7. Use your data table to plot a graph of V (vertical axis) versus /7 (horizontal). Graph 1: Total Voltage vs Total Current 2021-Oct01-BOL Page 5 of 9 Physics: Electricity WCLN.ca 8. Determine the slope and intercept for the graph above and write the equation of the line (y=mx+b is your starting point for all straight lines). Equation of line using variables from the graph (along with any constants) Rise 25 Slope: (show work and include units) run 1.5 Intercept (include units): 0 Equation of line: Y = 25 1.5 9. Re-examine your answers and relate to question (6) above. Discuss what the equation of your line represents? This equation gives a clear understanding of resistance. 10. What, precisely, does the slope represent? I he current or Voltage 1 1. Determine the unknown resistance, Rx, by examine your answers above and comparing to question (6). Unknown resistance, Rx (show all work below) R x = VX 25 = 104.2 I X 0. 24 RX= 104. 2 2 12. Right-click on resistor Rx to determine its actual value. How does it compare to your calculated value above? Determine the percentage error between your calculated value and the actual value. Percentage Error: %error Experimental Value - Actual Value | Actual Value X 100% 100 - 100 106 % error 0 2021-Oct01-BOL Page 6 of 9X WCLN.ca Part 2 1 Examine the resistance determined in part 1. Explain why the total resistance of the circuit, Ry, is less than any of the individual resistors, R;, R, or Rx. You will need to discuss the properties of a parallel circuit to explain this properly. In 0 pocallel Citcut , $he +ovol vesistonce iS5 Sways less thon the fesistonce amond Wi dual Pesistos. Discuss how your graph would change if you plotted V5 vs Ix. Describe its shape compared the original graph of Vy vs Ir. What would the slope of a graph of Vp vs Ix be? Plot the data for y vs Ix directly onto Graph I from part 1. Label it Ix. Imagine that you added another resistor connected in parallel to the above circuit. a. How would the graph of y vs It change? Explain why and confirm with the simulation. b. How would the graph of y vs Iy change? Explain why and confirm with the simulation. Imagine your original circuit. If you added another resistor connected in series (right after the battery and before the parallel section) a. How would the graph of y vs It change? Explain why and confirm with the simulation. b. How would the graph of vs Iy change? Explain why and confirm with the simulation. Carefully think about this one before you answer. 2021-0Oct01-BOL Page 7 of 9