Series Circuits 23 July 2005Professor Andrew H. Andersen 1ELEC 103Series Circuits23 July 2005 Series Circuits 2Objective• At the conclusion of this presentation the student will – Identify a series circuit– Apply Ohm’s law in series circuits– Determine and identify ground in a circuit– Determine total series resistance– Determine the current in a series circuit– Determine the total effect of voltage sources in series– Apply Kirchhoff’s voltage law– Use a series circuit as a voltage divider– Determine power in a series circuit– Apply the proper prefix for units of measurementSeries Circuits 23 July 2005Professor Andrew H. Andersen 223 July 2005 Series Circuits 3Series Circuit Characteristics1. The current is the same everywhere in the circuit. – This means that wherever I try to measure the current, I will obtain the same reading.2. Each component has an individual Ohm's law Voltage Drop. – This means that I can calculate the voltage using Ohm's Law if I know the current through the component and the resistance.3. Kirchoff's Voltage Law (KVL) applies. – This means that the sum of all the voltage sources is equal to the sum of all the voltage drops or– VS = V1 + V2 + V3 + . . . + VN4. The total resistance in the circuit is equal to the sum of the individual resistances.– RT = R1 + R2 + R3 + . . . + RN5. 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 + . . . + PN23 July 2005 Series Circuits 4Current in a Series Circuit• The current in a series circuit is the same through all points• The current through each resistor in a series circuit is the same as the current through all the other resistors that are in series with it• Current entering any point in a series circuit is the same as the current leaving that pointSeries Circuits 23 July 2005Professor Andrew H. Andersen 323 July 2005 Series Circuits 5Current in a Series CircuitCurrent in a series circuit is the same everywhere23 July 2005 Series Circuits 6Measuring Current in a Series CircuitIn a series circuit the location of the ammeter does not matterSeries Circuits 23 July 2005Professor Andrew H. Andersen 423 July 2005 Series Circuits 7Series Resistance Formula• Regardless of the number of individual resistors connected in series, the total resistance of a series circuit is the sum of each of the individual valuesRT = R1 + R2 + R3 + . . . + RN• The total resistance will always be larger than the largest individual resistor23 July 2005 Series Circuits 8Total Series Resistance• The total resistance of a series circuit is equal to the sum of the resistances of each individual series resistorSeries Circuits 23 July 2005Professor Andrew H. Andersen 523 July 2005 Series Circuits 9Resistors in Series• A series circuit provides only one path for current between two points so that the current is the same through each series resistor23 July 2005 Series Circuits 10Series Connected ResistanceRAB = R1 + R2RAB = R1 + R2 + R3 + R4RAB = R1 + R2 + R3Series Circuits 23 July 2005Professor Andrew H. Andersen 623 July 2005 Series Circuits 11Total Series ResistanceRT is not dependent on component order23 July 2005 Series Circuits 12Determining the Resistance on a Printed Circuit BoardTrace the path from one end to the other and draw it on paper as you goSeries Circuits 23 July 2005Professor Andrew H. Andersen 723 July 2005 Series Circuits 13Resistors on a Protoboard23 July 2005 Series Circuits 14Find R4RT = R1 + R2 + R3 + R4 R4 = RT -R1 -R2 -R3Series Circuits 23 July 2005Professor Andrew H. Andersen 823 July 2005 Series Circuits 15Find R4R4 = RT -R1 -R2 -R3R4 = 146kΩ – 10kΩ –33kΩ – 47kΩ56kΩ23 July 2005 Series Circuits 16Ohm’s Law in Series Circuits• Current through one of the series resistors is the same as the current through each of the other resistors and is the total current• If you know the total voltage and the total resistance, you can determine the current by using:• If you know the voltage drop across one of the series resistors, you can determine the current by using any of the following:TTV I = RR1 R2 R3 RN123N V V V V I = = = = RRRRSeries Circuits 23 July 2005Professor Andrew H. Andersen 923 July 2005 Series Circuits 17Ohm’s Law in Series Circuits• If you know the total current, you can find the voltage drop across any of the series resistors by using: VR= I R• The polarity of a voltage drop across a resistor is positive at the end of the resistor that is closest to the positive terminal of the voltage source• The direction of current (electron flow) through a resistor is from the negative end of the resistor to the positive end23 July 2005 Series Circuits 18Ohm’s Law in Series Circuits• An open (an open switch or circuit failure) in a series circuit prevents all current from flowing (R = 0Ω)I = 0A• In an open series circuit, there is zero voltage drop across each series resistor• The supply voltage appears across the open points in the circuitSeries Circuits 23 July 2005Professor Andrew H. Andersen 1023 July 2005 Series Circuits 19Sources Connected Series Aiding23 July 2005 Series Circuits 20Sources Connected Series OpposingVT = VS1 –VS2 + VS3Series Circuits 23 July 2005Professor Andrew H. Andersen 1123 July 2005 Series Circuits 21Kirchhoff’s Voltage Law• The algebraic sum of all voltages (both sources and drops) around a closed path is zeroΣV = 0 orVS –V1 –V2 –V3 -… -Vn = 023 July 2005 Series Circuits 22Kirchhoff’s Voltage Law• The algebraic sum of all the voltage drops around a single closed loop in a circuit is equal to the total source voltage in that loopVS= V1+ V2+ V3+ … + VnSeries Circuits 23 July 2005Professor Andrew H. Andersen 1223 July 2005 Series Circuits 23KVL∑∑SOURCES DROPSV = V 10V = 5.5V + 4.5V23 July 2005 Series Circuits 24Double Subscript NotationVABVBCVCDNode ReferencedVACSeries Circuits 23 July 2005Professor Andrew H. Andersen 1323 July 2005 Series Circuits 25Double Subscript NotationVAVBVCGround ReferencedVD = 0V23 July 2005 Series Circuits 26Calculate the Voltage DropsSeries Circuits 23 July 2005Professor Andrew H. Andersen 1423 July 2005 Series Circuits 27Power in a Series Circuit• The total amount of power in a series resistive circuit is equalto the sum of the powers in each resistor in seriesPS = P1 + P2 + P3 + . . . + PNVS I = V1 I + V2 I+ V3 I + . . . + VN II2 RT = I2 R1 + I2 R2 + I2 R3 + . . .