Week 8 Lab_ Circuits 2 with RC

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California Polytechnic State University, San Luis Obispo *

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Electrical Engineering

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Dec 6, 2023

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Electric Circuits, Part 2 GOALS ● Learn to apply Kirchhoff’s Loop Rule and Junction Rule to various circuits ● Learn to apply Ohm’s Law to resistors, and compare to experimental measurements ● To investigate and measure current and voltage for Resistor-Capacitor (RC) circuits EQUIPMENT ● variable-voltage power supply (0-6 V) ● multimeter ● 1 switch ● 1 single-pole double-throw switch ● 3 light bulbs (6 V) and holders ● 5 different resistors (10-100 ohms) ● 2 large capacitors (25,000 μF) ● Several alligator clip wires ● Several banana plug wires ● Two Differential Voltage probes ● Two Current probes ● Computer interface ● LoggerPro software ● Experiment file: OHMSLAW Activity 1: Kirchhoff’s Loop Rule Two resistors, in series 1. Build the following circuit using two resistors that have different resistance, one about twice the resistance of the other. 2. Turn on the variable power supply and turn it up to 6 volts. 3. Measure the potential difference across the power supply using a voltage probe and placing the red lead at point A and the black lead at point E. Record your value in the table below. 4. Next, we are going to move the leads around the circuit while keeping the orientation of the red leading the black . Place the black lead at point A and the red lead at point B. Record the potential difference. Record your value in the table below. 5. Place the black lead at point B and the red lead at point C. Record your value in the table below.

6. Place the black lead at C and the red lead at D. Record your value in the table below. 7. Place the black lead at D and the red lead at E. Record your value in the table below. Points compared Measured ∆V ∆ V AE = V A - V E 6V ∆ V BA = V B - V A 0V ∆ V CB = V C - V B -2.08V ∆ V DC = V D - V C -3.92V ∆ V ED = V E - V D 0V ∆ V AE + ∆ V BA + ∆ V CB + ∆ V DC + ∆ V ED = 0V ● Q1.1: What is the sum of all of the potential differences around the loop ABCDEA? What should it be according to Kirchhoff’s Loop Rule? The sum of all potential differences around the loop ABCDEA is 0V. According to Kirchoff’s Loop Rule, the sum should be 0V. ● Q1.2: Why was it important to preserve the relative orientation of the black and red leads in this measurement? Switching the orientation of the black and red leads would lead to a sign change in the voltage, making the sum of the potential difference not add up to 0V. 8. Given that the voltage at point E is zero, label the voltage at points A, B, C, and D on the diagram above . 9. Measure the current in the circuit: 0.1 A 10. Calculate the expected potential difference across each resistor using Ohm’s Law and complete the table below. Resistance Current Calculated ∆ V (∆ V = IR ) Measured ∆ V % difference 20 Ω .1 A -2 V -2.08 V 4% 40 Ω .1 A -4 V -3.92 V 2%

Activity 2: Adding a bulb, or resistor, in parallel to another Imagine that we hook up circuit shown. ● P2.1: Predict the order of the brightness of the bulbs when the switch is open? (i.e., write something like B 1 = B 2 < B 3 ) ? 1 = ? 2 > ? 3 ● P2.2: Predict the order of the brightness of the bulbs when the switch is closed? ? 1 > ? 2 = ? 3 Now build the circuit above and then test your predictions. Use a power supply with a fixed voltage and do not exceed 6 V. ● R2.1: Rank the brightness of the bulbs when the switch is open? ? 1 = ? 2 > ? 3 ● R2.2: Rank the brightness of the bulbs when the switch is closed? ? 1 > ? 2 = ? 3 ● Q2.1: When the switch is closed did the brightness of bulb B1 increase, decrease, or stay the same as compared to having the switch open? Why? When the switch was closed, the brightness bulb B1 increased. This is because when you close the switch, the total resistance of the circuit decreases, causing an increase in current, causing an increase in power.

We have seen that light bulbs do not have a constant resistance. So, to get quantitative we will now replace the bulbs with resistors which all have the same resistance. Rebuild the circuit. It should look like the figure to the right. Make the appropriate measurements so that you can fill in the following table. (You will need to use current and voltage probes to do this.) Switch open Switch closed I 1 0.016A 0.021A I 2 0.016A 0.01A I 3 0A 0.01A ∆ V 1 3.1V 4.09V ∆ V 2 3.1V 2.1V ∆ V 3 0V 1.91V ● Does current through resistor R 1 increase, decrease, or stay the same when the switch is closed? Explain. The current through resistor increases when the switch is closed because when you close the 𝑅 1 switch, resistance decreases so the current must increase. ● Does the potential difference (voltage) across resistor R 1 increase, decrease, or stay the same when the switch is closed? Explain. When the switch is closed, the voltage across increases… 𝑅 1

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