Kirchhoff's Rules Worksheet

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School

Northeastern University *

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Course

109

Subject

Electrical Engineering

Date

Feb 20, 2024

Type

pdf

Pages

Uploaded by KidIceAlligator10

Worksheet 8 - Kirchhoff's Circuit Rules Note: As we have been suggesting throughout this unit, it will help you to do as much of the worksheet as possible at the boards. ● Remember, Kirchhoff’s rules are used to solve the voltages and currents of a circuit. Each application of Kirchhoff’s Loop Rule and Kirchhoff’s Junction Rule gives you a new equation that can be used to solve a system of equations. ● Kirchhoff’s Loop Rule states that for any closed loop of a circuit, the total voltage change must equal zero. In other words, if you designate one point of the circuit to be at V=0, then if you make a closed loop around the circuit and total up all of those components, returning to the same spot as before will give you V=0. Think about this like going on a hike through mountainous terrain. If you start at your car and go on a hike, you will go through many elevation gains and elevation drops. However, if you return back to your car at the end, the total net elevation difference will be zero. ● Kirchhoff’s Junction Rule states that the amount of current that goes into a junction must be equal to the amount of current that leaves that junction. This is an application of conservation of charge: all electrons that come into a junction must also leave that junction. ● To solve a system of equations, you must have as many equations as you do unknown variables. For example, in a circuit in which you do not know three currents, you must construct three unique equations in order to solve the system of equations. ● When looking at a circuit, you may not know which direction the current is going before solving the circuit. This means that you do not know whether or not a voltage drop or a voltage gain will occur across a resistor. This is ok! At the end of the problem if you have labeled a current going the wrong way, the answer you will get will be negative; this is a sign that you should indicate your current going the other way. Page 1

Part 1: Series-Parallel combination circuits Consider the following circuit as our starting circuit. The purpose of this exercise is to help you understand how to break up a series-parallel combination circuit to find the current and potential difference across each resistor. To do this, we will first combine different resistors and then work our way back up. Think about how these four resistors are connected to each other. Which ones are in parallel and which ones are in series? Instructions - follow steps 1-3 to contract the circuit to one equivalent resistor. Then go back up (steps 4-7) to label every resistor in every diagram with its current and voltage. Step 1: Combine two resistors together first. Which two should you choose? Redraw the circuit with three resistors and label the resistors with their resistance. (To redraw, use the Google drawing below. Simply erase one resistor by putting a white box over it to have only three resistors.) Don’t worry about the current and voltage labels until step 6. Resistance calculation: Page 2

Step 2: Now, combine two more resistors together, and redraw the circuit with only two resistors. Again, use white boxes to cover up resistors you have merged and don’t need. You may need to then add a line to represent a wire. Use the voltage/current labels in step 5. Resistance calculation: Page 3

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