EE_220L2NicholasJavier

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EE 220L, Section #1003 Lab # 3: Basic DC Circuits, Part 2 09/20/23 Javier Correa-Martinez Nicholas Hong

2 Objective: The purpose of this lab is to design voltage and current dividers. We will also use Kirchoff ’ s Voltage and Current Laws to analyze resistive circuits. Equipment Used: Power Supply 30V Multimeter Breadboard 5k Ω ± 5% Resistor 3.5k Ω ± 5% Resistor 6.5k Ω ± 5% Resistor 2k Ω ± 5% Resistor 1k Ω ± 5% Resistor 10k Ω ± 5% Resistor 20k Ω ± 5% Resistor 100k Ω ± 5% Resistor 5.1k Ω ± 5% Resistor 51k Ω ± 5% Resistor Theory (Javier Correa-Martinez): To reduce a circuit's voltage, voltage dividers connect resistors in series. In order to divide an input current into branches of decreasing magnitudes, current dividers use resistors connected in parallel. According to Kirchhoff's voltage law, the total of all voltages in a loop is equal to zero. According to Kirchhoff's current law, the total amount of current flowing into a node is equal to zero. These laws and equations can be used to evaluate circuits and provide values for voltages and currents of any element that were previously unknown. Theory (Nicholas Hong): Voltage dividers use resistors connected in series in order to lower the voltage of a circuit. Current dividers use resistors connected in parallel in order to split an input current into branches of smaller magnitudes. Kirchhoff's voltage law states that the sum of all voltages in a loop is equal to zero, such that. Kirchhoff’s current law states that the sum of all currents entering a node is equal to zero, such that. Using these laws/equations to analyze circuits can produce values for previously unknown voltages and currents of any elements. Procedure: Part 1. Designing a Voltage Divider In this part of the lab, we used a 15V source and a 5 kΩ resistor to design a voltage dividing circuit with three total resistors. Across the 5 kΩ resistor there needs to be a voltage drop of 5V and the voltage drop needs to be 3.5V and 6.5V across the two unknown resistors. Then we chose resistors with values that are as close as possible to the calculated values in the previous steps using a 5% standard values chart. We then built the circuit and recorded the voltage drops across each resistor along with the

3 current though the circuit. Finally we calculated the expected voltages and the current using the new resistor values from the second step and compared them to the values from the circuit. Figure 1: Circuit 1 – Voltage Divider Table: Circuit 1 Values Resistors ( kΩ ) Calculated Voltage Drop (V) Measured Voltage Drop (V) Percent Difference 5 5 1.7696 64.61% 3.5 3.5 1.1541 67.03% 6.5 6.5 2.1711 66.60% Possible sources of discrepancies may have came from having resistors with values that were not as close as they could be with the calculated values. Part 2. Designing a Current Divider The next part of the lab was to use a 10V source and three resistors to design a current divider that supplies 2mA, 5mA, and 10mA to the three resistors in the circuit. Then, using the 5% values chart, we chose resistors with values as close as possible the those calculated in the previous step. Next we built the circuit and recorded the voltages across and the currents through each resistor in the circuit. After, we re calculated the expected voltages and currents using the new, standardized resistor values from the previous step and compared them to the measured values.

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4 Figure 2: Circuit 2 – Current Divider Table: Circuit 2 Values Resistors ( kΩ ) Expected Current (mA) Measured Current (mA) Expected Voltage (V) Measured Voltage (V) Current Percent Difference Voltage Percent Difference 5 2 1 10 5 50% 50% 2 5 2.5 10 5 50% 50% 1 10 4.65 10 4.65 53.5% 53.5% Percent discrepancies may be due to resistors with values that are not as close as possible to the calculated values. Question: If all the resistors in the current divider are scaled by a factor of ,k, how does this affect the current going through them? It will not affect the current going through them. Circuit 1: R T = 1 kΩ + 4.7 kΩ = 5.7 kΩ Percent difference = [5.7−5.646] 5.7 × 100 = 0.947% Circuit 2: R T = 1 kΩ + 4.7 kΩ + 8.2 kΩ = 13.9 kΩ Percent difference = [13.9−13.676] 13.9 × 100 = 1.61%

5 Part 3. Kirchoff ’ s Voltage Law. In the third part of the lab, we were given a circuit and asked to calculate the voltage drop across each resistor and the current through the circuit. Then we built the circuit and adjusted each power supply to 2.5V and connected them as shown. Next, we kept everything the same but adjusted one of the supplies to 0V and kept the other at 2.5V and recorded the current. After we returned the first supply back to 2.5 and lowered the other to 0 and recorded the current again. Figure 3: Circuit 3 Table: Circuit 3 Values Resistors ( kΩ ) Calculated Voltage Drops (mV) Measured Voltage Drops (mV) Percent Difference 2 75.76 79.25 4.61% 10 378.79 394.65 4.19% 20 757.58 808 6.66% 100 3.788 3.95 4.28% Table: Current Values Current 1 (mA) 0.02 Current 2 (mA) 0.0204 Sum of Current 1 and 2 (mA) 0.0404 Current When Supply is 2.5V (mA) 0.0402 Percent Difference 0.495%

6 Question: How does the sum of these two currents just recorded compare to the current measured when both supplies were set at 2.5V? Why? The sum of the two currents is very close to the current measured when both the supplies were set at 2.5V. This is due to the superposition theorem which states that in a circuit having multiple independent sources, the response of an element will be equal to the algebraic sum of the response of that element by considering one source at a time. Question: Can two independent voltage sources be placed in parallel? Why or why not? Two independent voltage sources cannot be placed in parallel as it would violate Kirchoff ’ s voltage Law. Question: Can two independent current sources be placed in series? Why or why not? Two independent current sources cannot be placed in parallel as it would violate Kirchoff ’ s Current Law. Part 4. Equivalent Circuits In the last part of the lab, we first calculated the equivalent-resistance circuit of Circuit 4 then determined the current that will flow into the equivalent circuit. Next, we built Circuit 4 and recorded the current delivered by the power supply to the current. After, we built the equivalent single resistor circuit with a resistor with a value as close to the equivalent resistance as possible and recorded the current delivered by the power supply. Finally, we compared the calculated current with the measured currents from step 3 and from the equivalent circuit built in step 4.

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7 Figure 4: Circuit 4 – Circuit for simplification Table: Circuit 4 Values Equivalent Resistance ( kΩ ) 2.312 Equivalent Current (mA) 6.487 Current Delivered by Power Supply (mA) 7.65 Current % Difference 15% The values from the calculated current and the measured currents from Circuit 4 have a percent difference of 15% which may be due to the physical equivalent resistor not being exactly the same as the calculated value. Conclusion (Javier Correa-Martinez): After completing this lab, we were able to configure a voltage divider and current divider and utilize Kirchhoff's voltage and current equations to determine the voltages and currents of unknown resistors. The voltage and current did not function as well as we thought it would based on the large percent discrepancies in some of the parts, although having a sizable error %. Kirchhoff's rules allowed us to precisely examine the voltages and currents in a circuit with a very little degree of inaccuracy. Sources of error in this lab may be due to the resistors used as it was not possible to get resistors with values that are the same as those calculated. Therefore we had to use resistors that were as close as possible to the calculated values which may have affected the current and voltages in the circuit. Despite this, our calculations were accurate and we were still able to compare them to the measured values

8 Conclusion (Nicholas Hong): In conclusion of this lab, we were able to connect a simple voltage divider and current divider, and we were able to use Kirchhoff’s voltage and current laws to analyze the voltages and currents of unknown resistors. Though with a significant error percentage, the voltage and current dividers were able to work in a lower magnitude than expected. With a minuscule amount of error, we were able to accurately analyze a circuit’s voltages and current using Kirchhoff’s laws. A potential source of error in our voltage and current dividers could be in our resistors. We were unable to find resistors that precisely matched our calculated resistance values, so we had to use similar resistors with a percent tolerance that included our calculated values. The tolerance percentage could potentially have caused a higher or lower voltage drop than anticipated. Errors in analyzing a circuit’s voltages and currents using Kirchhoff’s laws could be chalked up to imprecise voltage inputs from sources. We found that we were still accurate in our calculations compared to the measured values.