EE030LA Lab #2

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030

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Electrical Engineering

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Dec 6, 2023

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Christian Velasco: 862166334 Ryan Bordadora: 862226054 LAB 2: Kirchhoff’s Current and Voltage Laws Section 004 Tianchen Yang

Introduction The objectives of Lab 2 are: 1. Understanding of the origin of Kirchhoff’s Current Law (KCL); 2. Understanding of the equivalency in multiple formulations of KCL; 3. Validity of KCL formulated in terms of either actual or reference currents; 4. Experimental verification of Kirchhoff’s Current Law (KCL); 5. Measurement errors and basic error analysis; 6. Understanding of the origin of Kirchhoff’s Voltage Law (KVL); 7. Validity of KVL formulated in terms of either actual or reference voltages; 8. Experimental verification of the Kirchhoff’s Voltage Law (KVL); Theory Laboratory 1’s theoretical objectives are meant to teach us the following: Theoretical Concept: KCL and KVL ❖ KCL ➢ The sum of all current into a node and all current out of one equals 0 ➢ The convention is that the input is positive while the output is negative ❖ KVL ➢ The sum of the voltage in a loop is 0 ➢ The convention is that voltage rise is negative while a voltage drop is negative

Prelab 1. If Kirchhoff's Current Law were not to hold, what would this result in? Provide at least one example. If Kirchhoff’s law were to not hold then, it would result in outgoing current not being equal to incoming current. An example can be simply stated as in the theoretical background portion of the lab it gives an example of there being an uncontrollable accumulation of charge in this part of the conductor. 2. An ammeter measurement of current in some branch resulted in the current value -1.4 mA. Draw the direction of the reference current measured by the ammeter. What is the direction of the actual (true) current? See Figure P2. 3. Derive the KCL equation for the node in Figure P3. 𝑖 1 + 𝑖 2 + 𝑖 3 + 𝑖 4 = 0 4. The redundant node can be defined as a node which links at least one branch which doesn’t contain any elements. Would it be possible to write the KCL equation for a redundant node? Why? ‘ Yes, because current still flows through the wire, it would be just harder to determine the actual current. The main issue is that, unlike a standard current, the direction of the current’s flow is 5. Which law of nature would be violated if the Kirchhoff’s Voltage Law were not valid? Law of Energy Conservation 6. Assuming that v is the actual voltage between nodes 1 and 2, what will be the sign of voltage vE measured by a voltmeter? Refer to Figure P6 It will be negative. 7. Derive the KVL equation for loop 2 in Figure 2.4. − 𝑉 𝐸1 − 𝑉 𝐸2 + 𝑉 𝐸3 = 0 8. Refer to formula (2.16). Assume that voltmeter measurements for some closed

loop in a circuit resulted in a set of reference voltages VS = 5.02V, vR1 = -1.48V, vR2 = 2.51V, vR3 = 1.01V. The KVL equation for that loop was VS + vR1 - vR2 - vR3 = 0. What was the absolute relative error of the voltage measurements? 𝑉 𝐸???? = 5. 02𝑉 − 1. 48𝑉 − 2. 51𝑉 − 1. 01𝑉 =. 02𝑉 𝐸???? = 0.02𝑉 1.01𝑉 | | | | × 100% = 2% Lab 1.3 nominal [Ω] measured [Ω] max resistor power specification, Pmax [mW R1 5.1k 5.01k 250mW

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