# Ch. 20 Electric Circuits

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1 Ch. 0 Electric Circuits 0. Electromotive Force Every electronic device depends on circuits. Electrical energy is transferred from a power source, such as a battery, to a device, say a light bulb. Conducting wires Light bulb A diagram of this circuit would look like the following: Light - Battery Battery symbol nside a battery, a chemical reaction separates positive and negative charges, creating a potential difference. - This potential difference is equivalent to the battery s voltage, or emf (ε) (electromotive force). This is not really a force but a potential. Because of the emf of the battery, an electric field is produced within and parallel to the wires. This creates a force on the charges in the wire and moves them around the circuit. This flow of charge in a conductor is called electrical current ().

2 A measure of the current is how much charge passes a certain point in a given time: Electrical Current Δ q Δt Units? Charge time C s [ Ampere] [ A] f the current only moves in one direction, like with batteries, it s called Direct Current (DC). f the current moves in both directions, like in your house, it s called Alternating Current (AC). Light bulb Battery Electric current is due to the flow of moving electrons, but we will use the positive conventional current in the circuit diagrams. - e So shows the direction of positive charge flow from high potential to low potential.

3 0. Ohm s Law The flow of electric current is very analogous to the flow of water through a pipe: The battery pushing the current acts like the water pump pushing the water. The voltage of the battery is analogous to the pump pressure the higher the pump pressure, the faster can push the water through. h Thus, the larger my battery voltage, the greater my current. V Let s make this an equality: V R This is Ohm s Law. The proportionality constant, R, is called the electrical resistance. V Volts Amp V A Units? R [ Ohm ] [ Ω ] Define Resistor: A component of an electrical circuit that offers resistance to the flow of electric current.

4 Resistor, R Symbol for resistors: - Straight lines have essentially zero resistance ε V Resistivity The electrical resistance of a conductor depends on its shape: -Longer wires have more resistance -Fatter wires have less resistance Length R L A Thus,. Let s make this an equality: R L ρ A Cross-sectional area The proportionality constant, ρ, is the electrical resistivity. Units? ρ R A L Ω m m [ m] Ω

5 Resistivity is an intrinsic property of materials, like density: Every piece of copper has the same resistivity, but the resistance of any one piece depends on its size and shape. ρ,r R ρ, ρ, R

6 Clicker Question 0- A copper wire with a circular cross section has a resistance R. What would the resistance of the wire be if the radius of the wire was reduced by a factor of?. R. R 3. 4R 4. R/ 5. R/4

7 Temperature Dependence of Resistivity The resistance of most materials changes with temperature. For good conductors (metals) the resistance decreases with decreasing temperature. R Conductors R nsulators T T For insulators (poor conductors) the resistance increases with decreasing temperature. For many materials, we find that: R R [ α( T T ) ] o o R Resistance at temperature T R o Resistance at temperature T o α is the temperature coefficient of resistivity α > 0 α < 0 For metals tl For insulators

8 0.4 Electrical Power Power Work Time Our standard definition of power is:. So what would electrical power be? From the definition of potential: W V W q qv Thus, P qv t P V We can write this different ways using Ohm s Law, VR: P R P V R *So we have 3 ways of calculating electrical power depending on what other quantities are known.

9 Electrical Energy Work and Energy have the same units (Joules). Thus, Electrical companies, like Entergy, measure your monthly energy use this way, in units of kilowatt hours (kwh). Energy Power Time For example, if you used an average power of 500 W for 3 days (744 hours), your energy consumption would be: E (.5 kw)(744 h) 6 kwh At a cost of roughly \$0.3/kWh, this would be a monthly bill of \$45. 6 kwh J

10 Example: Two light bulbs, A and B, are connected to a 0-V outlet (a constant voltage source). Light bulb A is rated at 60 W and light bulb B is rated at 00 W. Which bulb draws the most current from the outlet?. A. B P V f P is bigger, than will be bigger for the same V.

11 0.5 Alternating Current When the voltage provided changes periodically with time! V V sin π ft 0 V / R sin π ft 0 V R Peak values f 60Hz 0 0 / Sinusoidal function frequency Power: P V V π ft sin 0 0 Mean Value of Power: P 0 V 0 rms V rms 0 V0 rms V rms root-mean square value

12 0.6 Series Circuits The first way is to wire them together in series: The same current runs through two components connected in series. V and V are called voltage drops. *We speak of currents running through resistors, and voltages drops across resistors. Thus, the current through resistor R is, and the voltage drop across R is V.

13 How would we find the net resistance (equivalent resistance, R eq ) for resistors connected in series? For resistors connected in series, the sum of the voltage drops across all the resistors must equal the battery voltage. Thus, V V V But from Ohm s Law: R eq R R R eq R R R R Thus, for resistors wired up in series, the equivalent resistance is: R eq R R R3 i.e. you just add them!!!

14 Clicker Question 0-4 What is the current in the following circuit? 4 Ω Ω V A. 00A A A

15 0.7 Parallel Circuits For resistors connected in parallel, the voltage drop across each resistor is the same. The current through each might be different. t splits:. Thus, V V V. From Ohm s Law: R V V eq V V V R R R R R Thus, R eq R R R 3 for resistors in parallel.

16 Clicker Question 0-5 Given the circuit below, a larger current flows through which h resistor? Ω 4 Ω - V V. R. R 3. The current through each is the same.

17 0.8 Series and Parallel Circuits Now let s hook resistors up both in series and in parallel in the same circuit! What is the current in the following circuit? We need to find the equivalent resistance! Thus, R eq 40 Ω V Req 4 0. A 40

18 Clicker Question 0-6 What is the equivalent resistance between points A and B? 8.00 Ω. Ω. 4 Ω 3. 6 Ω 4. 8 Ω

19 Three identical light bulbs are connected to a battery as shown in the diagram. What happens when bulb #3 burns out?. Bulbs and both get brighter. Bulb gets brighter and stays the same 3. Bulb gets dimmer and gets bi brighter 4. Bulb gets dimmer and stays the same # # #3 -

20 C Q Tot Q Q V C V C C ) V C eq V C Thus, C eq C C C C3 ( - V To find the equivalent capacitance for capacitors wired in parallel, you just add them! Now consider two capacitors wired in series: Thus, C C The voltage across each will now, in general, be different, but the charge on each of the plates must be the same. V V - V C C eq V V V C C C *Notice that these rules are just the opposite for resistors in combination. 3 Q Q C ( ) Q C C C Q ( ) V C V C C eq For capacitors wired in series, the reciprocal of the equivalent capacitance is just the sum of the reciprocal capacitances.

21 Clicker Question 0-7 What is the equivalent capacitance between points A and B?. 0.5 μf. μf μf 4. 6 μf

22 Clicker Question 0-7 (cont.) Let s first number the capacitors: Capacitors, 4, and 6 are in series, thus: C C C C C μf Now the circuit looks like this: μf Now capacitor 3 is in parallel with capacitor 46: C C C Now the circuit looks like this: μf Now capacitors,346, and 5 are in series: C C C 346 C 5 5 C.0 F 5 C eq 3456 μ

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