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Chapter 19 DC Circuits

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Objective of the Lecture Explain Kirchhoff’s Current and Voltage Laws. Demonstrate how these laws can be used to find currents and voltages in a circuit. Explain how these laws can be used in conjunction with Ohm’s Law.

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19.3 Kirchhoff’s Rules Some circuits cannot be broken down into series and parallel connections.

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Kirchhoff’s Rules Loop 1 Loop 2 ii i i i1i1 i2i2 i2i2 Many practical resistor networks cannot be reduced to simple series-parallel combinations (see an example below). Terminology: -A junction in a circuit is a point where three or more conductors meet. -A loop is any closed conducting path. junction

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Basic Laws of Electric Circuits Nodes and Branches: A node: A node can be defined as a connection point between two or more branches. A branch: A branch is a single electrical element or device. A circuit with 5 branches. A circuit with 3 nodes. 2

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Kirchhoff's Rules Junction rule. The sum of the magnitudes of the currents directed into a junction equals the sum of the magnitudes of the currents directed out of the junction. Loop rule. Around any closed circuit loop, the sum of the changes in potential around any closed path of a circuit must be zero.

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Kirchhoff’s Current Law Or KCL for short (Junction Rule) –Based upon conservation of charge – the algebraic sum of the charge within a system can not change. Where N is the total number of branches connected to a node.

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Kirchhoff’s Voltage Law Or KVL for short (Loop Rule) –Based upon conservation of energy – the algebraic sum of voltages dropped across components around a loop is zero. Where M is the total number of branches in the loop.

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Junction Rule Junction rule. The sum of the magnitudes of the currents directed into a junction equals the sum of the magnitudes of the currents directed out of the junction.

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Application of Junction Rule Q: A galvanometer with a full-scale limit of 0.100 mA is to be used to measure a current of 60.0 mA. How much current will pass through the shunt resistance R? A: 60.0 – 0.1 = 59.9 mA A galvanometer is a type of sensitive ammeter: an instrument for detecting electric current.

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Current Measurement

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2/13/07184 Lecture 2012 Multi-Loop Circuits Assume we have a junction point a We define a current i 1 entering junction a and two currents i 2 and i 3 leaving junction a Kirchhoff’s Junction Rule tells us that

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19.3 Kirchhoff’s Rules For these circuits we use Kirchhoff’s rules. Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it.

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19.3 Kirchhoff’s Rules Loop rule: The sum of the changes in potential around a closed loop is zero.

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Loop Rule Loop rule. Around any closed circuit loop, the sum of the potential drops equals the sum of the potential rises.

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Voltage Measurement

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Putting it all together

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Kirchhoff’s Rules Kirchhoff’s junction rule The algebraic sum of the currents into any junction is zero:

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Kirchhoff’s Rules Kirchhoff’s loop rule The algebraic sum of the potential differences in any loop, including those associated with emfs and those of resistive elements, must equal zero.

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Kirchhoff’s Rules Rules for Kirchhoff’s loop rule

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Kirchhoff’s Rules Rules for Kirchhoff’s loop rule (cont’d)

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Kirchhoff’s Rules Solving problems using Kirchhoff’s rules

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Kirchhoff’s Rules Example 1

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Kirchhoff’s Rules Example 1 (cont’d)

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Kirchhoff’s Rules Example 1 (cont’d)

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Find all the currents including directions. Loop 1 Loop 2 ii i i i1i1 i2i2 i2i2 Kirchhoff’s Rules Example 2 Loop 1Loop 2 multiply by 2 i = i 1 + i 2

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27 Ammeter and Voltmeters A device used to measure current is called an ammeter A device used to measure voltage is called a voltmeter To measure the current, the ammeter must be placed in the circuit in series To measure the voltage, the voltmeter must be wired in parallel with the component across which the voltage is to be measured Voltmeter in parallel High resistance since you do not want current going through it Ammeter in series Low resistance since current goes through it

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Practice Problem p.548 #23 Calculate the current in the circuit of Fig. 19–43 and show that the sum of all the voltage changes around the circuit is zero.

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Practice Problem p.548 #24

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19.3 Kirchhoff’s Rules Problem Solving: Kirchhoff’s Rules 1. Label each current. 2. Identify unknowns. 3. Apply junction and loop rules; you will need as many independent equations as there are unknowns. 4. Solve the equations, being careful with signs.

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Homework: Problems 25 and 32

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Closure: Kahoot: 19-3

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