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Electrical Engineering

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Dec 6, 2023

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Physics Lab (Online Simulation) 1 OHM’S LAW - KIRCHOFF’S LAW Electricity and Light TA name: Tej Raj Karki Due Date: 10/5/2023 Student Name: Alberto Canales Theory: A D.C. circuit consists of sources of direct current (EMFs), connected to a network of elements. If the ele ments are ohmic (obey Ohm’s Law) then the currents through the elements are directly proportional to the voltages applied across the elements. For ohmic elements, the relation between the current through an element (I), in amps, and the voltage across the element (V), in volts, is V = IR [1] where R is the resistance of the element in ohms. Resistors, which are commonly used in electronic devices, are ohmic. If two or more resistors are connected in series with a voltage source, as illustrated in Figure 18-1, they collectively behave as an equivalent single resistor with resistance, R ser , where R ser = R 1 + R 2 + R 3 +  + R n [2] Figure 18-1 the resistors are connected in parallel to the voltage source, as illustrated in Figure 18-2, then they collectively behave as an equivalent single resistor with a resistance, R par , where R 1 R 2 R 3 R n V

Physics Lab (Online Simulation) 2 Figure 18-2 n 3 2 1 par R 1 R 1 R 1 R 1 R 1 + + + + =  [3] The circuits illustrated in Figures 18-1 and 18-2 can be reduced to a single loop containing a single voltage source and a single resistor. And Ohms Law can be used to determine the currents in the circuit. If however the circuit contains more than one voltage source in a network of resistors, the circuit usually cannot be reduced to a single loop. Kirchhoff’s rules are useful in a nalyzing a multi-loop circuit. This Prelab is worth 15 points Type all your answers in Blue (1) Write down an equation and solve for the total resistance of three resistors R 1 =100 Ω , R 2 =150 Ω, R 3 =350Ω in the resistors were arranged in the following combinat ion: a) All three in series (1 point) R = R1 + R2 + R3 100Ω + 150Ω + 350Ω = 600Ω b) All three in parallel (1 point) R = (R1*R2*R3)/(R1 + R2 + R3) R = ((100Ω )( 150Ω )( 350Ω )) /(100Ω + 150Ω + 350Ω) = 8750Ω c) How would you arrange these three resistors to get a net resistance of 410 Ω. (1 point) R = ((R1*R2)/(R1 + R2 )) + R3 (((100Ω)(150Ω))/(100Ω + 150Ω)) + 350 =410Ω (2) If you have an experimental setup which has three unknowns, how many linearly independent equations do you need to determine the unknowns to find one unique solution? (1 point) You need three equations (3) What is Kir choff’s law of current? What does it conserve? (1 point) The Kirchoff’s law of current is the total sum of all currents entering a junction and conserves charge V R n R 3 R 2 R 1

Physics Lab (Online Simulation) 3 (4) What is Kirchoff’s law of vol tage? What does it conserve? (1 point) The Kirchoff’s law of vol tage is the total sum of voltages in a closed loop and conserves potential energy (5) Electrical circuits have two main problems: “Short” and “Open”. Define these two conditions with diagram and an example showing the consequence of each of these faults. (Use back of the page if necessary). (2+2 = 4 points) Open: The circuit stops which breaks due to the circuits loop being open Short: A short circuit is when the current goes through a different path on the circuit and has no flow on that path

Physics Lab (Online Simulation) 4 (6) Apply Kirchoff’s law of current and voltage in loop 1 and loop 2 of the above circuit and write down the corresponding equation. (2.5 + 2.5 = 5 points) Loop I: Current equation : I3 = I2 + I1 Voltage equation: 0 = ((I3)(R3)) - V1 + ((I1)(R1)) Loop 2: Current equation: I3 = I2 + I1 Voltage equation: 0 = ((I3)(R3)) - V2 +((I2)(R2)) Part A: Ohm’s Law This lab uses the Ohm’s Law and Circuit Construction Kit DC simulation from PhET Interactive Simulations at University of Colorado Boulder, under the CC-BY 4.0 license. https://phet.colorado.edu/sims/html/ohms-law/latest/ohms-law_en.html https://phet.colorado.edu/sims/html/circuit-construction-kit-dc/latest/circuit-construction-kit-dc_en.html Develop your understanding: Open Ohm’s Law , then explore to develop your own ideas about how resistance, current, and battery voltage are related. R 1 R 2 R 3 I 1 I 2 I 3 V 1 V 2 I 2 I 1 Loop 1 Loop 2

Physics Lab (Online Simulation) 5 1. As you change the value of the battery voltage, how does this change the current through the circuit and the resistance of the resistor? If the current or resistance remains constant, why do you think it is? → As you change the voltage, the current increases too and resitance stays constant. If current stays constant then resistance will increase with the voltage. I think this happens because as V increases, one variable has to increase in change to offset the other variable. 2. As you change the value of the resistance of the resistor, how does this change the current through the circuit and the battery voltage? If the current or voltage remains constant, why do you think? → If the voltage stays constant, resistance and current are inversly porportional so when resistance increases, current decreases. If the current stays constant, resistance and voltage are directly porportional so when resistance increases, voltage increases. 3. Use understanding to make predictions about a circuit with lights and batteries. → The more lights you add to the series, the less bright it will be → The more batteries you add to the series, the more bright it will be Demonstrate your understanding: Directions: As you answer the questions, explain in your own words why your answer makes sense and provide evidence from your #1 experiments. Add more experiments to #1 if you need to get better evidence.

Physics Lab (Online Simulation) 6 2. If you change the value of the battery voltage: a. How does the current through the circuit change? (answer, explain) When the resistance is constant, the current is directly porportional to the voltage so if voltage increases, the current increases. b. How does the resistance of the resistor change? (answer, explain) When the current is constant, the resistance is directly porportional to the voltage so if voltage increases, the resistance increases. 3. If you change the resistance of the resistor: a. How does the current through the circuit change? (answer, explain) When the voltage is constant, the resistance is inversely porportional to the current so if resistance increases, the current decreases. b. How does the voltage of the battery change? (answer, explain) When the current is constant, the resistance is directly porportional to the voltage so if resistance increases, the voltage increases.

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