Preamble. Kirchoff Voltage Law (KVL) Series Resistors. In this section of my lectures we will be. resistor arrangements; series and

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1 Preamble Series and Parallel Circuits Physics, 8th Edition Custom Edition Cutnell & Johnson Chapter , 0.0 Pages 60-68, 69-6 n this section of my lectures we will be developing the two common types of resistor arrangements; series and parallel. To do this we will introduce some very important laws and rules that you must become familiar with. (. Bolton - 0) Series and Parallel Circuits (. Bolton - 0) Series and Parallel Circuits Physics 55.3: ntroduction to Electricity and Magnetism Physics 55.3: ntroduction to Electricity and Magnetism Series esistors The figure shows a series resistor circuit. Our first job is to determine how the two series resistors combine to form an equivalent resistor. Note: n this circuit the same current flows through each of the resistors. Kirchoff oltage Law (KL) Around any closed-circuit loop, the sum of the potential drops equals the sum of the potential rises. An alternative way of stating KL is loop 0 (. Bolton - 0) Series and Parallel Circuits 3 (. Bolton - 0) Series and Parallel Circuits 4 Physics 55.3: ntroduction to Electricity and Magnetism 3 Physics 55.3: ntroduction to Electricity and Magnetism 4

2 Note that only voltage sources (i.e., a battery) are considered as a potential rise. This is due to the convention of considering how positive charge is affected when going around a circuit. Since positive charge gains potential when going from a negative terminal on the voltage source to the positive terminal on the voltage source it experiences a potential rise. f this is the case, where are the potential drops in the loop shown above? The figure is redrawn showing polarity information (. Bolton - 0) Series and Parallel Circuits 5 (. Bolton - 0) Series and Parallel Circuits 6 Physics 55.3: ntroduction to Electricity and Magnetism 5 Physics 55.3: ntroduction to Electricity and Magnetism 6 Series esistance Using Ohm s Law Using Kirchoff s oltage Law (KL) loop 0 earranging (and using Ohm s Law) ( ) where series series esistors in series (i.e., resistors with the same current flowing through them) add. series 3 n Note: f the resistors do not have the same current flowing through them they are NOT in series! (. Bolton - 0) Series and Parallel Circuits 7 (. Bolton - 0) Series and Parallel Circuits 8 Physics 55.3: ntroduction to Electricity and Magnetism 7 Physics 55.3: ntroduction to Electricity and Magnetism 8

3 Example Series esistor oltages Example Using Ohm s Law s (4.00, 8.00) s ( ) ( 0 Ω 0 Ω ) A Ω Ω 0.4A 0Ω 4.0 What is the voltage across each resistor? 0.4A 0Ω 8.0 (. Bolton - 0) Series and Parallel Circuits 9 (. Bolton - 0) Series and Parallel Circuits 0 Physics 55.3: ntroduction to Electricity and Magnetism 9 Physics 55.3: ntroduction to Electricity and Magnetism 0 Note that it is possible to determine the voltage across each resistor in a series combination by recalling that the same current goes through each series resistor and that t the sum of fthe resistor voltages must equal the battery voltage. Take for example the resistor from the previous circuit: (. Bolton - 0) Series and Parallel Circuits But the current is equal to Therefore earranging (. Bolton - 0) Series and Parallel Circuits Physics 55.3: ntroduction to Electricity and Magnetism Physics 55.3: ntroduction to Electricity and Magnetism

4 oltage Divider ule (D) (for series resistors) The voltage across any resistor in a series combination of resistances is equal to the voltage across the series combination multiplied by the value of the resistor in question over the total series resistance. Example oltage Divider Circuit What is the voltage across the 4.7kΩ resistor? (. Bolton - 0) Series and Parallel Circuits 3 (. Bolton - 0) Series and Parallel Circuits 4 Physics 55.3: ntroduction to Electricity and Magnetism 3 Physics 55.3: ntroduction to Electricity and Magnetism 4 Example (.6) Example 3 ery mportant Circuit ()!!! What is the value of E for 0mA to flow in the circuit (in the direction shown)? What is A? B? AB? (. Bolton - 0) Series and Parallel Circuits 5 (. Bolton - 0) Series and Parallel Circuits 6 Physics 55.3: ntroduction to Electricity and Magnetism 5 Physics 55.3: ntroduction to Electricity and Magnetism 6

5 Procedure Before going too far consider s the circuit a series circuit? s the circuit a parallel circuit? What is the direction of the current? What is the symbol on the bottom left? What does it do? What are the polarities of the voltage drops across the resistors? Example 3 (50,-7,57) (. Bolton - 0) Series and Parallel Circuits 7 (. Bolton - 0) Series and Parallel Circuits 8 Physics 55.3: ntroduction to Electricity and Magnetism 7 Physics 55.3: ntroduction to Electricity and Magnetism 8 Parallel esistors The figure shows a parallel resistor circuit. Our first job is to determine how the two parallel resistors combine to form an equivalent resistor. Note: n this circuit the same voltage is across each of the resistors. (. Bolton - 0) Series and Parallel Circuits 9 Kirchoff s Current Law (KCL) At any circuit node, the sum of the currents into the node equals the sum of the currents out of the node. Note: Currents out of the node are considered positive and currents into the node are considered as negative. An alternative way of stating KCL is node 0 (. Bolton - 0) Series and Parallel Circuits 0 Physics 55.3: ntroduction to Electricity and Magnetism 9 Physics 55.3: ntroduction to Electricity and Magnetism 0

6 The figure is redrawn showing current information Using Ohm s Law But Therefore (. Bolton - 0) Series and Parallel Circuits (. Bolton - 0) Series and Parallel Circuits Physics 55.3: ntroduction to Electricity and Magnetism Physics 55.3: ntroduction to Electricity and Magnetism Using Kirchoff s Current Law (KCL) node 0 earranging Using Ohm s Law (again) n order for this equation to be true (i.e., ) ) ll l parallel parallel (. Bolton - 0) Series and Parallel Circuits 3 (. Bolton - 0) Series and Parallel Circuits 4 Physics 55.3: ntroduction to Electricity and Magnetism 3 Physics 55.3: ntroduction to Electricity and Magnetism 4

7 Parallel esistance esistors in parallel (i.e., resistors with the same voltage across them) do NOT add. parallel 3 n Note: f the resistors do not have the same voltage across them they are NOT in parallel! Two resistors in parallel t turns out that we have two resistors in parallel a lot of the time in the circuits we use. The previous formula can be simplified to parallel (. Bolton - 0) Series and Parallel Circuits 5 (. Bolton - 0) Series and Parallel Circuits 6 Physics 55.3: ntroduction to Electricity and Magnetism 5 Physics 55.3: ntroduction to Electricity and Magnetism 6 Example 4 Parallel esistor Currents Example 4 (.A, 0.6A) What is the total current and the current through each of the resistors? (. Bolton - 0) Series and Parallel Circuits 7 Using Ohm s Law parallel parallel 30 Ω. 8A 0 Ω 0 Ω and. A 0Ω 0. 6A 0Ω (. Bolton - 0) Series and Parallel Circuits 8 Physics 55.3: ntroduction to Electricity and Magnetism 7 Physics 55.3: ntroduction to Electricity and Magnetism 8

8 Note that it is possible to determine the current through each resistor in a parallel combination by recalling that the same voltage is across each parallel resistor and that the sum of the resistor currents must equal the total current. Take for example the resistor from the previous example: But the total current is equal to ( parallel ) earranging and substituting for ( ) parallel (. Bolton - 0) Series and Parallel Circuits 9 (. Bolton - 0) Series and Parallel Circuits 30 Physics 55.3: ntroduction to Electricity and Magnetism 9 Physics 55.3: ntroduction to Electricity and Magnetism 30 Current Divider rule (CD) (for parallel resistors) The current through any resistor in a parallel combination of resistances is equal to the total current through the parallel combination multiplied by the value of the equivalent resistance of the parallel resistors over the value of the resistor in question. Two esistors in Parallel t turns out that we have two resistors in parallel a lot of the time in the circuits we use. The previous formula can be simplified Does this make sense? (. Bolton - 0) Series and Parallel Circuits 3 (. Bolton - 0) Series and Parallel Circuits 3 Physics 55.3: ntroduction to Electricity and Magnetism 3 Physics 55.3: ntroduction to Electricity and Magnetism 3

9 Example 5 Parallel esistor Current Example 5 (.3mA) What is the current through the 4.7kΩ resistor? Before going too far, think about it (. Bolton - 0) Series and Parallel Circuits 33 (. Bolton - 0) Series and Parallel Circuits 34 Physics 55.3: ntroduction to Electricity and Magnetism 33 Physics 55.3: ntroduction to Electricity and Magnetism 34 Example 6 ery mportant Circuit ()!!! What is ab? Procedure Before going too far consider s the circuit a series circuit? s the circuit a parallel circuit? What is the value of s? What is the symbol on the bottom left? What does it do? Can there be more than one in a circuit? What is the polarity of the voltage, ab? (. Bolton - 0) Series and Parallel Circuits 35 (. Bolton - 0) Series and Parallel Circuits 36 Physics 55.3: ntroduction to Electricity and Magnetism 35 Physics 55.3: ntroduction to Electricity and Magnetism 36

10 Example 6 (0) (. Bolton - 0) Series and Parallel Circuits 37 Physics 55.3: ntroduction to Electricity and Magnetism 37