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. Resistor Switch WireBattery Voltmeter Ammeter A Conductor of Current Opens and Closes Circuits Provides Resistance to Current Flow Source of DC Charge Flow Measures Current Measures Voltage

More Circuit Symbols Here are some additional circuit symbols that you may see. Potentiometer AC Source Ground Crossing Junction Capacitor Diode Stores Charge on Plates Variable Resistor Provides AC Current Drains Excess Charge Buildup Only Allows Current to Flow One Way All Four Wires Connect 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 PictureCircuit 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.

A series circuit is similar to a one lane road, current can flow in only one path. Even if you add a 2 nd resistor in series, there is still just 1 path. Series Circuit R1R1 R2R2

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? R1 V R2 I

Series Circuit How do we find R eq ? R2 R1 V I Divide both sides by I s R eq V

The Series Circuit (cont.) Every series configuration can be reduced to a single value for resistance known as the equivalent resistance, or R eq. The formula for R eq is as follows for series: This can be used as a step to solve for the current in the circuit or the voltage across each resistor. R1R1 R2R2 R eq I

Sample Problem (Series) A circuit is configured in series as shown below. –What is the equivalent resistance (R eq )? –What is the current through the circuit? (Hint: Use Ohm’s Law.) 10  20  30  6V I eq = 0.1A 60  6V

Sample Problem (Series) (cont.) We still have one question to ask. What are the voltages across each resistor? –For the 10  Resistor: –For the 20  Resistor: –For the 30  Resistor: What do you notice about the voltage sum? 10  20  30  6V I eq = 0.1A Voltages across resistors in series add to make up the total voltage.

Series Circuit Summary Current is constant throughout the entire circuit. Resistances add to give R eq. Voltages across each resistor add to give V eq.

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 I1I1 I2I2

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 Parallel Circuit R2R2 R1R1

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. R1R1 R2R2 Branch X X A break in one of the branches of a parallel circuit will not disable current flow in the remainder of the circuit.

Parallel Circuit How do we find R eq a parallel circuit? R2 V Divide both sides by V p R eq V R1R1 R2R2 V Use Ohm’s law

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. An equivalent resistance (R eq ) can also be found for parallel configurations. It is as follows: R1R1 R2R2 R eq

Parallel Circuit video Clip

Sample Problem (Parallel) A circuit is configured in parallel as shown below. –What is the equivalent resistance of the circuit?  30  6V 12  6V

Sample Problem (Parallel) What is the current in the entire circuit? What is the current across each resistor?  30  6V The 30  ResistorsThe 60  Resistor

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. –The Inverses of the Resistances add to give the inverse of R eq. –Current through each resistor adds to give I eq. –Make use of Ohm’s Law.

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. R1R1 R2R2 R3R3 R4R4 Series Parallel

Sample Problem (Combo) What is the equivalent resistance (R eq ) of the circuit? –First, we must identify the various combinations present. Series Parallel SeriesParallel 10  40  30  10  20  25V

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 Parallel 10  40  30  10  20  25V 40  10  25V Series 50 

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? 40  10  25V Series 50  25V

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.

25V 30  10  20  15V

25V 30  10  30  15V

24μf 12μf 36μf

220V 114    117        220V 114    117      140     