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Electrical Circuits ~Moving Charge Put to Use The Circuit • All circuits, no matter how simple or complex, have one thing in common, they form a complete loop. • As mentioned before, circuits should have various circuit elements in the loop. Circuit Symbols • Each circuit element has its own symbol. • Common circuit symbols are shown below. Wire Battery A Conductor of Current Switch Source of DC Charge Flow Ammeter Opens and Closes Circuits Resistor Measures Current Voltmeter Provides Resistance to Current Flow Measures Voltage More Circuit Symbols • Here are some additional circuit symbols that you may see. Capacitor Diode Stores Charge on Plates Potentiometer Variable Resistor Only Allows Current to Flow One Way Junction All Four Wires Connect AC Source Provides AC Current Ground Drains Excess Charge Buildup Crossing Wires Only Cross and do not Connect. Circuit Diagrams • Circuit diagrams use circuit symbols instead of drawing an actual picture for each circuit. • This simplifies and standardizes circuit pictures. Circuit Picture Circuit Diagram (Schematic) Series Circuit • Have you ever driven down a 1 lane road? • You can keep moving until… • If there is an accident all traffic stops, there is no other road to follow. Series Circuit • A series circuit is similar to a one lane road, current can flow in only one path. • Even if you add a 2nd resistor in series, there is still just 1 path. R1 R2 Terminal Voltage • Terminal voltage is the voltage supplied outside of the source • This is ONLY the same as the EMF if there is no internal resistance Series Circuit • One path means all components have the same current • What is the voltage drop across R1? Vsource VR1 VR 2 R1 V I VR1 IR1 VR 2 IR2 R2 Series Circuit • How do we find Req? Vseries VR1 VR 2 I s R e q I s R1 I s R2 Divide both sides by Is R e q R1 R2 R1 V I V R2 Req The Series Circuit (cont.) • Every series configuration can be reduced to a single value for resistance known as the equivalent resistance, or Req. • The formula for Req is as follows for series: Req R1 R2 • This can be used as a step to solve for the current in the circuit or the voltage across each resistor. R1 I Req R2 Sample Problem (Series) • A circuit is configured in series as shown below. – What is the equivalent resistance (Req)? 10W Req R1 R2 R3 Req 10W 20W 30W 20W 6V Req 60W – What is the current through the circuit? (Hint: Use Ohm’s Law.) Req Veq I eq I eq 6V I eq 60W I eq 0.1A Veq 30W Ieq = 0.1A Req 6V 60W Sample Problem (Series) (cont.) • We still have one question to ask. What are the voltages across each resistor? V R V IR I Voltages across – For the 10W Resistor: V IR V 0.1A10W V 1V – For the 20W Resistor: V IR V 0.1A 20W resistors in series add to make up the total voltage. V 2V – For the 30W Resistor: V IR V 0.1A 30W V 3V • What do you notice about the voltage sum? 6V Ieq = 0.1A 10W 20W 1V 2V 3V 6V 6V Veq 30W Series Circuit Summary • Current is constant throughout the entire circuit. I eq I1 I 2 • Resistances add to give Req. Req R1 R2 • Voltages across each resistor add to give Veq. Veq V1 V2 Devices that Make Use of the Series Configuration • Although not practical in every application, the series connection is crucial as a part of most electrical apparatuses. – Switches • Necessary to open and close entire circuits. – Dials/Dimmers • A type of switch containing a variable resistor (potentiometer). – Breakers/Fuses • Special switches designed to shut off if current is too high, thus preventing fires. – Light Strands • Prevents all bulbs from going out when a single one burns out. The Parallel Circuit (cont.) • Parallel circuits are similar to rivers with branches in them. • The current from the river divides into multiple paths. • After the paths, the water recombines into the same amount of flowing water. I eq I1 I 2 Ieq Ieq I1 I2 Parallel Circuit • A parallel circuit is similar to a river that branches, current can flow in multiple paths. • Once the paths end, the total flow remains the same R1 R2 The Parallel Circuit • Notice that the circuit branches out to each resistor, allowing multiple paths for current to flow. • If there are exactly two clear paths from the ends of one resistor to the ends of the other resistor. A break in one of the branches of a parallel circuit will not disable current flow in the remainder of the circuit. Branch X R1 R2 X Branch Parallel Circuit • How do we find Req a parallel circuit? I parallel I R1 I R 2 Vp R eq Vp R1 Use Ohm’s law Vp 1 1 1 R e q R1 R2 R2 Divide both sides by Vp V V R1 R2 R2 V Req The Parallel Circuit (cont.) • Notice how every resistor has a direct connection to the DC source. This allows the voltages to be equal across all resistors connected this way. Veq V1 V2 • An equivalent resistance (Req) can also be found for parallel configurations. It is as follows: 1 1 1 Req R1 R2 R1 R2 Req Parallel Circuit video Clip Sample Problem (Parallel) • A circuit is configured in parallel as shown below. – What is the equivalent resistance of the circuit? 1 1 1 1 Req R1 R2 R3 1 1 1 1 Req 30W 30W 60W 1 Req 1 1 1 30 W 30 W 60 W Req 12W 6V 6V 30W 30W 60W 12W Sample Problem (Parallel) • What is the current in the entire circuit? Req Veq I eq I eq Veq Req 6V I eq 12W I eq 0.5 A • What is the current across each resistor? The 30W Resistors V I R 6V The 60W Resistor 6V I 30W 6V I 60W I 0.2 A I 0.1A 30W 30W 60W Parallel Circuit Summary • There are several facts that you must always keep in mind when solving parallel problems. – Voltage is constant throughout the entire parallel circuit. Veq V1 V2 – The Inverses of the Resistances add to give the inverse of Req. 1 1 1 Req R1 R2 – Current through each resistor adds to give Ieq. I eq I1 I 2 – Make use of Ohm’s Law. R V V I V IR I R Devices that Make Use of the Parallel Configuration • Although not practical or safe in every application, the parallel circuit finds definite use in some electrical apparatuses. – Electrical Outlets • Constant voltage is a must for appliances. – Light Strands • Prevents all bulbs from going out when a single one burns out. – Voltmeters • Since voltage is constant in parallel, these meters must be connected in this way. Combination Circuits • Parallel Paths: Must make a complete loop through two resistors with out touching any other component. • Series Paths: Must form a path through multiple resistors with out crossing an intersection. Combination Circuits • Some circuits have series/parallel combinations • These can be reduced using equivalent resistance formulas. • Now let’s solve a problem involving this circuit. R2 R1 Series R3 Parallel R4 Sample Problem (Combo) What is the equivalent resistance (Req) of the circuit? – First, we must identify the various combinations present. Series Parallel Req R1 R2 Req 10W 30W Req 40W Parallel 25V 1 1 1 Req R1 R2 1 1 1 Req 20W 20W Req 10W Series 20W 10W 20W 30W 10W 40W Sample Problem (Combo) • The simplified circuit only shows the equivalent resistances. Is the circuit now fully simplified? • Now, we must identify the final configuration. Series Req R1 R2 Req 40W 10W Req 50W 25V 10W 40W Parallel 25V 50W Series 20W 10W 20W 30W 10W 40W Sample Problem (Combo) • The circuit is further simplified below. Can it be simplified again? • Now, the circuit is completely simplified. • What is the current in the entire circuit? Req Veq I eq I eq Veq 25V I eq 50W Req I eq 0.5 A Series 25V 10W 40W 50W 25V 50W Lights demo • • • • DC source with 3 lights in series DC source with 3 lights in parallel DC source with 2 lights in series 1 parallel DC source with 1 lights in series 2 parallel Conclusion • In order to approach any circuit problem, you must know the circuit symbols well. • All the circuits that you will be given will be series, parallel, or a combination of both that is solvable. • Ultimately, keeping a working knowledge of the properties of each circuit type is key. You may want to make a note card that contains all of these facts. 15V 25V 20W 10W 30W 20W 15V 25V 30W 10W 30W 12μf 24μf 36μf 151W 130W 120W 131W 114W 140 W 220V 44W 117W 107W 126W 77W 113W 26W