Parallel Circuits 5 February 2004Professor Andrew H. Andersen 1ELEC 103Parallel Circuits5 February 2004 Parallel Circuits 2Objectives• Identify a parallel circuit• Determine the voltage across each parallel branch• Apply Kirchhoff’s Current Law• Determine total parallel resistance• Apply Ohm’s law in a parallel circuit• Use a parallel circuit as a current divider• Determine power in a parallel circuitParallel Circuits 5 February 2004Professor Andrew H. Andersen 25 February 2004 Parallel Circuits 3Characteristics of the Parallel Circuit• The voltage across each component (branch) is the same everywhere in the circuit. – This means that wherever I try to measure the voltage, I will obtain the same reading, and this is the supply voltage.• Each branch has an individual current path. – We may calculate the branch current using Ohm's Law if we know the voltage across the component and the resistance.• Kirchoff's Current Law Applies. This means that the sum of all the currents entering a node is equal to the sum of all the currents leaving the node IT = I1 + I2 + I3 + . . . + IN• The inverse of the total resistance in the circuit is equal to inverse the sum of the inverse of the individual resistances.• The sum of the power supplied by the source is equal to the sum of the power dissipated in the components.PT = P1 + P2 + P3 + . . . + PN T123 N 1 1 1 1 1 = + + + ... + R R R R R 5 February 2004 Parallel Circuits 4Identifying Parallel Circuits• There is more than one current path (branch) as we move from one source terminal to the other (between two separate points)• The voltage between these two points also appears across each of the branches, then there is a parallel circuit between those two points• Each current path is called a branch• A parallel circuit is one that has more than one branchParallel Circuits 5 February 2004Professor Andrew H. Andersen 35 February 2004 Parallel Circuits 5Application of a Parallel Circuit• All lights and appliances in a home are wired in parallel• The switches are located in series with the lights5 February 2004 Parallel Circuits 6Application of a Parallel Circuit• An advantage of a parallel circuit over a series circuit is thatwhen one component (branch) of the circuit opens the other branches are not affectedParallel Circuits 5 February 2004Professor Andrew H. Andersen 45 February 2004 Parallel Circuits 7Voltage in a Parallel Circuit5 February 2004 Parallel Circuits 8Voltage in Parallel Circuits• The voltage across any branch of a parallel circuit is equal to the voltage across all of the other branches in parallelParallel Circuits 5 February 2004Professor Andrew H. Andersen 55 February 2004 Parallel Circuits 9Parallel Circuit5 February 2004 Parallel Circuits 10Voltage in a Parallel CiruitParallel Circuits 5 February 2004Professor Andrew H. Andersen 65 February 2004 Parallel Circuits 11Determining the Resistance on a Printed Circuit Board5 February 2004 Parallel Circuits 12Kirchhoff’s Current Law• Kirchhoff’s current Law (KCL) can be stated as:ΣI = 0The algebraic sum of all the currents entering and leaving a node is equal to zeroΣIin = ΣIoutThe algebraic sum of all the currents entering a node is equal to the algebraic sum of all the currents leaving a nodeI = 400mAParallel Circuits 5 February 2004Professor Andrew H. Andersen 75 February 2004 Parallel Circuits 13Kirchhoff’s Current Law (KCL)• The sum of the currents entering a node (total current in) is equal to the sum of the currents leaving that node (total current out)ΣIIN = ΣIOUTIIN1 + IIN2 + . . . + IINn = IOUT1 + IOUT2 + . . . + IOUTnIT = I1 + I2 + I3 + … + In5 February 2004 Parallel Circuits 14KCL• KCL at Node AΣIIN = ΣIOUTIT = I1 + I2 + I3• KCL at Node BΣIIN = ΣIOUTI1 + I2 + I3 = ITParallel Circuits 5 February 2004Professor Andrew H. Andersen 85 February 2004 Parallel Circuits 15KCL5 February 2004 Parallel Circuits 16Find ITParallel Circuits 5 February 2004Professor Andrew H. Andersen 95 February 2004 Parallel Circuits 17Find I25 February 2004 Parallel Circuits 18What is the Reading of Meters A3 and A5Parallel Circuits 5 February 2004Professor Andrew H. Andersen 105 February 2004 Parallel Circuits 19What is the Reading of Meters A3 and A5At X: IT –IR1 –IA3 = 0IA3 = IT –IR1 = 5mA – 1.5mAIA3 = 3.5mAAt Y: IA3 –IR2 –IA5 = 0IA5 = IA3 –IR2 = 3.5mA – 1mAIA3 = 2.5mAIA3 = 3.5mA IA5 = 2.5mA5 February 2004 Parallel Circuits 20Total Parallel Resistance• When two or more resistors are connected in parallel, the total resistance of the circuit (REQ) decreases• The total resistance of a parallel circuit is always smaller than the value of the smallest resistor• The equation to find the equivalent (total) resistance of a parallel circuit is:⎛⎞⎜⎟⎜⎟⎜⎟⎝⎠EQ 1 2 3 NEQ123 N 1 1 1 1 1 = + + + ... + R R R R R 1 R = 1 1 1 1 + + + ... + R R R RParallel Circuits 5 February 2004Professor Andrew H. Andersen 115 February 2004 Parallel Circuits 21Shorthand Notation for Parallel Resistors• A quick way to indicate 5 resistors connected in parallel, is:R1//R2//R3//R4//R55 February 2004 Parallel Circuits 22Resistors in Parallel• The total (equivalent) resistance for two resistors in parallel is equal to the product of the two resistors divided by the sum of the two resistors• The total (equivalent) resistance for three resistors in parallel is:EQ 1 212EQ12 1 1 1 = + R R R RR R = R + REQ 1 2 3123EQ12 23 1 3 1 1 1 1 = + + R R R R R R R R = RR + RR + R RParallel Circuits 5 February 2004Professor Andrew H. Andersen 125 February 2004 Parallel Circuits 23Resistors in Parallel• The total (equivalent) resistance for two resistors in parallel is equal to the product of the two resistors divided by the sum of the two resistors• If R1 = R2 then:EQ 1 212EQ12 1 1 1 = + R R R RR R = R + R211 1EQ11 11EQ RR R R = = R + R 2R R R = 25 February 2004 Parallel Circuits 24Find REQParallel Circuits 5 February 2004Professor Andrew H. Andersen 135 February 2004 Parallel Circuits 25Find REQSince all resistors are the same value: TTT R R = ; where N is the number of resistorsN 100Ω R = R = 520Ω 5 February 2004 Parallel Circuits 26Find All CurrentsParallel Circuits 5 February 2004Professor Andrew H. Andersen 145 February 2004 Parallel Circuits