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Circuit Examples By observing and participating in this lesson, you will be able to: Identify and describe series and parallel circuits. Simplify those circuits. Calculate the current and/or voltage of each part of a circuit. 1/81 Series and Parallel Circuits Electrical components can be connected in various ways. This drastically changes the properties of the circuit. 2/81 Series Circuits One simple way to arrange components in an electrical circuit is to create one large continuous loop with the components: switch 2 batteries Light bulb resistor 3/81 This is similar to a TV series where one episode follows another. Parallel Circuits Another way to connect a circuit is in parallel. In this arrangement, each component is connected separately in its own “loop”. 2 batteries 3 resistors in parallel 4/81 Resistors in Parallel To find the equivalent resistance of resistors added in parallel: 1 1 1 1 ... RP R1 R 2 R 3 Parallel or total combined resistance, Ω 5/81 Individual resistors, Ω Parallel Resistor Example Calculate the total effective resistance of two 10 Ohm resistors connected in parallel. 1 1 1 RP R1 R 2 1 1 1 R P 10Ω 10Ω 1 2 R P 10Ω RP 5Ω 6/81 Combine, use common denominator if needed Take the reciprocal of each side of equation Parallel Resistor Observations 5 Ohms. Notice that the total overall resistance is lower than either one of them individually! This occurs because there are multiple paths for the electrons to take, lowering their resistance. 7/81 Circuit Problems This section will detail how to calculate the various electrical quantities in a circuit. 8/81 Series Circuit R2=10Ω Calculate the current and electric potential difference for each component of the circuit shown. 5V R1=5Ω A good first step is to simplify the circuit. 9/81 Circuit Simplification 5V R1=5Ω 5V R S R1 R 2 R 3 ... R S 5Ω 10Ω 15Ω 10/81 Rs=15Ω R2=10Ω Because this is a series circuit, to combine the resistors and simplify the circuit, they are merely added together. 5V Rs=15Ω Current in a Series Circuit V IR V I R 5V I .33A 15Ω Use the voltage of the power supply and the total resistance of the circuit to find the total current flowing through the circuit. Because the electron flow has no where else to go, this amount is also the current flowing through both resistors. I1 and I2 is that same .33 Amperes. 11/81 R2=10Ω Voltage in a Series Circuit 5V Since we know the current flowing through each resistor, we can use Ohm’s law to find the potential difference for each of those resistors. R1=5Ω V1 IR V 2 IR V1 (.33A)(5Ω ) V2 (.33A)(10Ω ) V2 3.33V V1 1.67V 12/81 Notice how the sum of the two voltages adds up to the power supply for the circuit. Parallel Circuit Calculate the current and electric potential difference for each component of the circuit shown. 5V R1=5Ω R2=10Ω Notice how this parallel circuit contains the exact same components as the series circuit, they are just arranged differently. 13/81 Again, a good first step is to simplify the circuit. Circuit Simplification 5V R1=5Ω 1 1 1 RP R1 R 2 1 3 R P 10Ω 1 1 1 R P 5Ω 10Ω 10 RP Ω 3.3Ω 3 1 2 1 R P 10Ω 10Ω 14/81 R2=10Ω Notice this parallel resistance is less than either one individually. Shortcut Formula An equivalent formula can be used for two resistors, R1 and R2, connected in parallel. Sometimes this formula is easier to manipulate. R 1R 2 RP R1 R 2 It may be easier to remember this formula as the product over the sum for the two resistors. 15/81 Voltage in a Parallel Circuit 5V R1=5Ω R2=10Ω The easy part about any parallel circuit is the voltage applied to each item. Since each item has its own independent connection to the battery or power supply, each item receives that potential. In this case, V1 and V2 are each 5V. 16/81 Current in a Parallel Circuit 5V R1=5Ω R2=10Ω Once you realize that the electric potential for each resistor is 5V, finding the current is easy using Ohm’s law, V=IR. 17/81 V1 I1 R1 V2 I2 R2 5V I1 1A 5Ω 5V I2 .5A 10Ω Current Observations 5V R1=5Ω R2=10Ω Notice the two currents add up to the same value as the total current in the circuit. This is a good way to check your work. V 5V IT 1.5A R T 3.3Ω IT I1 I2 1A .5A 1.5A 18/81 Conclusion You should now be able to describe series and parallel circuits with words and numbers! Questions??? Homework: Check with your instructor 19/81