* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Review - Worth County Schools
Galvanometer wikipedia , lookup
Schmitt trigger wikipedia , lookup
Power electronics wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Negative resistance wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Operational amplifier wikipedia , lookup
Surface-mount technology wikipedia , lookup
Surge protector wikipedia , lookup
Power MOSFET wikipedia , lookup
Charlieplexing wikipedia , lookup
Electrical ballast wikipedia , lookup
RLC circuit wikipedia , lookup
Opto-isolator wikipedia , lookup
Two-port network wikipedia , lookup
Current source wikipedia , lookup
Rectiverter wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Current mirror wikipedia , lookup
Introducing Current and Direct Current Circuits Cells cell battery Cells Produce a voltage (called an EMF, or Electromotive Force, or e). EMF depends on chemistry of cell. A perfect cell would produce a terminal (or actual) voltage equal to its EMF. Terminal voltage is generally less than the EMF. Sample Circuit V light bulb V cell Series Circuit Only one path for the electricity to travel through. Good, because battery lasts longer. Bad, because the lights are dimmer and if one blows, they all blow. Parallel Circuit Multiple paths for the electricity to flow through. Good, because the lights are brighter, and if one blows, the others will remain lit. Bad, because the battery will be drained faster. Conductors Conduct electricity easily. Have high “conductivity”. Have low “resistivity”. Metals are examples. Insulators Don’t conduct electricity easily. Have low “conductivity”. Have high “resistivity”. Rubber is an example. Resistivity / Conductivity Depends on the identity of the material, not its shape, size, or configuration. Available in tables of data. Resistors Devices put in circuits to reduce the current flow. Built to provide a measured amount of “resistance” to electrical flow, and thus reduce the current. Resistors V V V Ohm’s Law Resistance in circuit causes potential to drop V = IR Voltmeter Measures voltage. Placed across a load or power source when current is flowing V V cell light bulb Ohmmeter Measures Resistance Placed across resistor when no current is flowing W Ammeter Measures Current Series Connection Low Resistance A Power in Electrical Circuits P = I V P: power (W) I: current (A) V: potential difference (V) 2 IR P = P = V2/R Electrical Circuit Symbols Electrical circuits often contain one or more resistors grouped together and attached to an energy source, such as a battery. The following symbols are often used: Ground + - + - + - + - Battery + - Resistor Resistances in Series Resistors are said to be connected in series when there is a single path for the current. I R1 VT R2 R3 Only one current For series connections: The current I is the same for each resistor R1, R2 and R3. The energy gained through E is lost through R1, R2 and R3. The same is true for voltages: I = I 1 = I 2 = I3 = V1 + V2 + V3 VT Equivalent Resistance: Series The equivalent resistance Re of a number of resistors connected in series is equal to the sum of the individual resistances. VT = V1 + V2 + V3 ; (V = IR) I R1 VT R2 R3 Equivalent Resistance ITRe = I1R1+ I2R2 + I3R3 But . . . IT = I1 = I2 = I3 Re = R1 + R2 + R3 Example 1: Find the equivalent resistance Re. What is the current I in the circuit? Re = R1 + R2 + R3 2W 3W 1W 12 V Re = 3 W + 2 W + 1 W = 6 W Equivalent Re = 6 W The current is found from Ohm’s law: V = IRe V 12 V I Re 6 W I=2A Example 1 (Cont.): Show that the voltage drops across the three resistors totals the 12-V emf. 2W 3W 1W 12 V Re = 6 W I=2A Current I = 2 A same in each R. V1 = IR1; V2 = IR2; V3 = IR3 V1 = (2 A)(1 W) = 2 V V1 + V2 + V3 = VT V1 = (2 A)(2 W) = 4 V 2 V + 4 V + 6 V = 12 V V1 = (2 A)(3 W) = 6 V Check ! Parallel Connections Resistors are said to be connected in parallel when there is more than one path for current. Parallel Connection: 2W 4W 6W Series Connection: 2W 4W 6W For Parallel Resistors: V2 = V4 = V6 = VT I 2 + I 4 + I 6 = IT For Series Resistors: I 2 = I 4 = I 6 = IT V2 + V4 + V6 = VT Equivalent Resistance: Parallel VT = V1 = V2 = V3 I T = I1 + I 2 + I3 Ohm’s law: Parallel Connection: VT V I R VT V1 V2 V3 Re R1 R2 R3 The equivalent resistance for Parallel resistors: R1 R2 R3 1 1 1 1 Re R1 R2 R3 N 1 1 Re i 1 Ri Example 3. Find the equivalent resistance Re for the three resistors below. N 1 1 Re i 1 Ri VT R1 2W R2 4W R3 6W 1 1 1 1 Re R1 R2 R3 1 1 1 1 0.500 0.250 0.167 Re 2 W 4 W 6 W 1 0.917; Re 1 Re 1.09 W 0.917 Re = 1.09 W For parallel resistors, Re is less than the least Ri. Example 3 (Cont.): Assume a 12-V emf is connected to the circuit as shown. What is the total current leaving the source of emf? VT R1 2W R2 4W R3 6W VT = 12 V; Re = 1.09 W V1 = V2 = V3 = 12 V IT = I1 + I2 + I3 12 V Ohm’s Law: V I R VT 12 V Ie Re 1.09 W Total current: IT = 11.0 A Example 3 (Cont.): Show that the current leaving the source IT is the sum of the currents through the resistors R1, R2, and R3. VT R1 2W R2 4W R3 6W V1 = V2 = V3 = 12 V IT = I1 + I2 + I3 12 V 12 V I1 6A 2W IT = 11 A; Re = 1.09 W 12 V I2 3A 4W 6 A + 3 A + 2 A = 11 A 12 V I3 2A 6W Check ! Short Cut: Two Parallel Resistors The equivalent resistance Re for two parallel resistors is the product divided by the sum. 1 1 1 ; Re R1 R2 Example: VT R1 6W R2 3W R1 R2 Re R1 R2 (3 W)(6 W) Re 3W 6 W Re = 2 W Series and Parallel Combinations In complex circuits resistors are often connected in both series and parallel. R1 In such cases, it’s best to use rules for series and parallel resistances to reduce the circuit to a simple circuit containing one source of emf and one equivalent resistance. VT R2 VT R3 Re Example 4. Find the equivalent resistance for the circuit drawn below (assume VT = 12 V). 4W VT 3W R3,6 6W (3 W)(6 W) 2W 3W 6 W Re = 4 W + 2 W Re = 6 W 4W 12 V 2W 12 V 6W Example 3 (Cont.) Find the total current IT. Re = 6 W 4W VT 3W 6W VT 12 V I Re 6 W IT = 2.00 A 4W 12 V 2W 12 V IT 6W Example 3 (Cont.) Find the currents and the voltages across each resistor. I4 = IT = 2 A 4W VT 3W 6W V4 = (2 A)(4 W) = 8 V The remainder of the voltage: (12 V – 8 V = 4 V) drops across EACH of the parallel resistors. V3 = V6 = 4 V This can also be found from V3,6 = I3,6R3,6 = (2 A)(2 W) (Continued . . .) Example 3 (Cont.) Find the currents and voltages across each resistor. V4 = 8 V V6 = V3 = 4 V V3 4 V I3 R3 3 W V6 4 V I6 R6 6 W I3 = 1.33 A 4W VT I6 = 0.667 A 3W I4 = 2 A Note that the junction rule is satisfied: SI (enter) = SI (leaving) I T = I4 = I 3 + I 6 6W Resistors in series R1 R2 R3 Req = R1 + R2 + R3 Req = SRi Resistors in parallel R1 R2 R3 1/Req = 1/R1 + 1/R2 + 1/R3 1/Req = S(1/Ri ) Kirchoff’s st 1 Rule Junction rule. The sum of the currents entering a junction equals the sum of the currents leaving the junction. Conservation of… charge. Kirchoff’s nd 2 Rule Loop rule. The net change in electrical potential in going around one complete loop in a circuit is equal to zero. Conservation of energy.