Lab #1 EES 512

Department of Physics Course Number EES 512 Course Title Physics waves and fields Semester/Year Fall 2023 Instructor TA Name Lab/Tutorial Report No. lab 1 Report Title Ohm’s law, Series Circuits, Kirchhoff’s Voltage Law, Parallel Circuits and Kirchhoff’s Current Law Section No. 42 Group No. N/A Submission Date 2023 Due Date September 27th 2023 Student Name Student ID Signature* Micheal Wojcik xxxx77384 MW (Note: remove the first 4 digits from your student ID) *By signing above you attest that you have contributed to this submission and confirm that all work you have contributed to this submission is your own work. Any suspicion of copying or plagiarism in this work will result in an investigation of Academic Misconduct and may result in a “0” on the work, an “F” in the course, or possibly more severe penalties, as well as a Disciplinary Notice on your academic record under the Student Code of Academic Conduct, which can be found online at: http://www.ryerson.ca/content/dam/senate/policies/pol60.pdf

Introduction: Ohm’s law, Series Circuits, Kirchhoff’s Voltage Law, Parallel Circuits and Kirchhoff’s Current Law are important topics related to electrical circuits and are needed to be discussed before the introduction into other topics related to electrical circuits. As such this lab is meant for the observation of all the aforementioned topics to gain a better understanding of topics taught in lectures. Theory: Ohm’s law: “ Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperatures remain constant ” ( 2 ). Ohm’s law can only be true if all factors remain constant.” V = IR, where V is the voltage across the conductor, I is the current flowing through the conductor and R is the resistance provided by the conductor to the flow of current ” ( 2 ). Series Circuits: A series circuit is an electrically conducting pathway where the entire current flows through each component. The total current in a series circuit is equal to the current through any resistor in the series, while the total resistance in a series circuit is the sum of the resistors. The total voltage in a series circuit is the sum of individual voltage drops across the resistors. Kirchhoff’s Voltage Law: Kirchhoff's circuit laws, first published in 1845, focus on energy and charge conservation in electrical circuits. They are derived from James Clerk Maxwell's differential equations, but Maxwell's differential equations were not published until 1861 and 1862. Kirchhoff used Georg Ohm's work for Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). Kirchhoff's laws are crucial for analyzing closed circuits, such as a circuit with five resistors in series and parallel arrangements. By analyzing the circuit's parameters using the resistor values, Kirchhoff's rules can determine the circuit's parameters, including the sources of voltage, such as batteries. Parallel Circuits: A parallel circuit is an electrical path that divides current, allowing only part to flow through any branch. The voltage across each branch remains constant, but currents may vary. In a home electrical circuit, the same voltage is applied across each light or appliance, but each load draws a different amount of current. Multiple batteries connected in parallel provide greater current than a single battery, but the voltage remains constant. Kirchhoff’s Current Law: “ Gustav Kirchhoff’s Current Law is one of the fundamental laws used for circuit analysis. His current law states that for a parallel path the total current entering a circuit's junction is exactly equal to the total current leaving the same junction. This is because it has no other place to go as no charge is lost ” (6) .

manual. Use the same resistances as before, R1 = 4.7 kΩ, R2 = 6.8 kΩ and R3 = 10 kΩ. Set the power supply voltage to 20 V. Measure the currents through each of the three resistors ( , and 𝑖 1 𝑖 2 ) as well as the total current through all three resistors ( ). Make sure you place the ammeter in 𝑖 3 𝑖 𝑇 series with the resistor whose current you wish to measure by disconnecting the wire to that resistor and inserting the ammeter there (in series). Record your measurements in Table 3. Data: 1.1: Table 1 Voltage Across Resistor ( ) 𝑉 𝑅 2.0V 5.0V 10V 15V 20V 25V Current Through Resistor (i) 0.43 mA 1.079 mA 2.16 mA 3.24 mA 4.325 mA 5.378 mA (𝑉 𝑅 )/𝑖 4.65 𝑘Ω 4.63 𝑘Ω 4.62 𝑘Ω 4.62 𝑘Ω 4.62 𝑘Ω 4.648 𝑘Ω 1.2: Table 2 𝑅 𝑇 (𝑚?𝑎?𝑢???) 𝑅 1 𝑅 2 𝑅 3 21.146 𝑘Ω 4.623 𝑘Ω 6.679 𝑘Ω 9.844 𝑘Ω 𝑉 𝑇 (𝑚?𝑎?𝑢???) 𝑉 1 𝑉 2 𝑉 3 19.999 19.999 19.999 19.999 1.3: Table 3 𝑅 𝑇 (𝑚?𝑎?𝑢???) 𝑅 1 𝑅 2 𝑅 3 2.1386 𝑘Ω 4.6232 𝑘Ω 6.679 𝑘Ω 9.844 𝑘Ω

𝑖 𝑇 (𝑚?𝑎?𝑢???) 𝑖 1 𝑖 2 𝑖 3 9.3390 mA 4.3360 mA 2.9984 mA 2.0280 mA Analysis: 1.1: Wrap Up questions: 1.1: After calculating the average of Table 1 and the graph, the average of both is roughly (𝑉 𝑅 )/𝑖 4.62 . The nominal value of the resistor is 4.7 , therefore there is a difference of 0.08 𝑘Ω 𝑘Ω 𝑘Ω between the calculated values and nominal value. The calculated values for both the table and graph are 4.62 which prove ohm’s law as all conditions remained constant and gave the same 𝑘Ω answer (give or take 0.01 ). 𝑘Ω

(4) Libretexts. (2020). Accessed September 25th 2023, 20.3: Kirchhoff’s Rules. Physics LibreTexts. 20.3: Kirchhoff’s Rules - Physics LibreTexts (5) The Editors of Encyclopaedia Britannica. (2023, September 15). Accessed September 25th 2023, Parallel circuit | Definition & Facts. Encyclopedia Britannica. https://www.britannica.com/technology/parallel-circuit (6) Storr, W. (2022). Accessed September 25th 2023, Kirchhoff’s Current Law. Basic Electronics Tutorials. https://www.electronics-tutorials.ws/dccircuits/kirchhoffs-current-law.html