~Moving Charge Put to Use 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. These vary depending on the design of the circuit. Zap! V A

Circuit Symbols A V Each circuit element has its own symbol. Common circuit symbols are shown below. Wire Battery A Conductor of Current Source of DC Charge Flow Switch Ammeter Opens and Closes Circuits Measures Current A Resistor Voltmeter Provides Resistance to Current Flow Measures Voltage V

More Circuit Symbols Here are some additional circuit symbols that you may see. Capacitor Diode Stores Charge on Plates Only Allows Current to Flow One Way Potentiometer Junction Variable Resistor All Four Wires Connect AC Source Provides AC Current Crossing Ground Wires Only Cross and do not Connect. Drains Excess Charge Buildup

Circuit Diagram (Schematic) Circuit diagrams employ the use of the circuit symbols as opposed to drawing an actual picture for each circuit. This simplifies and standardizes circuit pictures. Compare the picture below to the circuit diagram below. Circuit Picture Circuit Diagram (Schematic) A V V A

The Series Circuit Look at the circuit below. Two resistors are connected in a series configuration. Notice there is only one path for current to flow. There are no branches in the circuit, which would allow charge to take multiple paths. Since there is only one path, the current everywhere in the circuit is constant, even through the resistors. R1 R2 Click on the circuit to make a charge move through it along the single path. A break at any point in the circuit will result in the stoppage of current flow.

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: This can be used as a step to solve for the current in the circuit or the voltage across each resistor. R1 R2 Req

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

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

Series Circuit Summary There are several facts that you must always keep in mind when solving series problems. Current is constant throughout the entire circuit. Resistances add to give Req. Voltages across each resistor add to give Veq. Make use of Ohm’s Law.

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. Ammeters Since current is constant in series, these current-measuring devices must be connected in that configuration as well. 20 20A 20A A

The Parallel Circuit Look at the circuit below. The resistors have been placed in a parallel configuration. Notice that the circuit branches out to each resistor, allowing multiple paths for current to flow. One way to test if two resistors are in parallel is to see if there are exactly two clear paths from the ends of one resistor to the ends of the other resistor. Branch X A break in one of the branches of a parallel circuit will not disable current flow in the remainder of the circuit. Click on the circuit to animate current taking multiple paths. R1 R2

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 (Req) can also be found for parallel configurations. It is as follows: R1 R2 Req

The Parallel Circuit (cont.) Do you like rivers? Parallel circuits are kind of like rivers with branches in them. Is the current in each branch equal to the total current of the river? No, the total current is equal to the sum of the current in each branch. Thus, the individual currents add to form the total current. Ieq I1 I2

Sample Problem (Parallel) A circuit is configured in parallel as shown below. What is the equivalent resistance of the circuit? 12W 6V 30W 60W 6V

Sample Problem (Parallel) What is the current in the entire circuit? What is the current across each resistor? The 30W Resistors The 60W Resistor 30W 60W 6V

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 Req. Current through each resistor adds to give Ieq. 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. V

Combination Circuits Some circuits, such as the one shown below, have series/parallel combinations in their configurations. Many of these can be reduced using equivalent resistance formulas, while some cannot. Do you see the combinations within this circuit? Now let’s solve a problem involving this circuit. Parallel R2 R1 R3 R4 Series

Sample Problem (Combo) A combination circuit is shown below. What is the equivalent resistance (Req) of the circuit? First, we must identify the various combinations present. Series Parallel Parallel 30W 10W 20W 25V Series 10W 40W

Sample Problem (Combo) The simplified circuit only shows the equivalent resistances. Is the circuit now fully simplified? No, we must identify the final configuration. What is it? It’s a series configuration. Series 40W 10W 25V Parallel 50W 30W 10W 20W 25V Series 10W 40W

Sample Problem (Combo) The circuit is further simplified below. Can it be simplified again? No, the circuit is completely simplified. What is the current in the entire circuit? 40W 10W 25V Series 50W 50W 25V

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.