* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Short Version : 25. Electric Circuits
Ground (electricity) wikipedia , lookup
Fault tolerance wikipedia , lookup
Ground loop (electricity) wikipedia , lookup
Voltage optimisation wikipedia , lookup
Electrical ballast wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Electrical substation wikipedia , lookup
Stray voltage wikipedia , lookup
Electric battery wikipedia , lookup
Two-port network wikipedia , lookup
Surface-mount technology wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Mains electricity wikipedia , lookup
Buck converter wikipedia , lookup
Integrated circuit wikipedia , lookup
Current source wikipedia , lookup
Opto-isolator wikipedia , lookup
Surge protector wikipedia , lookup
Alternating current wikipedia , lookup
Flexible electronics wikipedia , lookup
Rectiverter wikipedia , lookup
Short Version : 25. Electric Circuits Electric Circuit = collection of electrical components connected by conductors. Examples: Man-made circuits: flashlight, …, computers. Circuits in nature: nervous systems, …, atmospheric circuit (lightning). 25.1. Circuits, Symbols, & Electromotive Force Common circuit symbols All wires ~ perfect conductors V = const on wire Electromotive force (emf) = device that maintains fixed V across its terminals. E.g., batteries (chemical), generators (mechanical), photovoltaic cells (light), cell membranes (ions). m~q Collisions ~ resistance g~E Ideal emf : no internal energy loss. Lifting ~ emf Energy gained by charge transversing battery = q E ( To be dissipated as heat in external R. ) Ohm’s law: I E R 25.2. Series & Parallel Resistors Series resistors : I = same in every component Same q must go every element. E V1 V2 I R1 I R2 I Rs Rs R1 R2 n For n resistors in series: I n=2: V1 R1 R1 R 2 E E Rs Rs R j Vj I Rj V2 R2 R1 R 2 E j 1 Rj Rs E Voltage divider Real Batteries Model of real battery = ideal emf E in series with internal resistance Rint . I means V drop I Rint Vterminal < E E I Rint I R L I E R int R L VRL RL Rint R L E E RL Example 25.2. Starting a Car Your car has a 12-V battery with internal resistance 0.020 . When the starter motor is cranking, it draws 125 A. What’s the voltage across the battery terminals while starting? Battery terminals E I R int I R L RL E 12 V Rint 0.020 I 125 A 0.096 0.020 0.076 Voltage across battery terminals = E Vint 12 V 125 A 0.020 9.5 V Typical value for a good battery is 9 – 11 V. Parallel Resistors Parallel resistors : V = same in every component I I1 I 2 E E E Rp R1 R 2 1 1 1 R p R1 R 2 For n resistors in parallel : Rp R1 R 2 R1 R 2 n 1 1 Rp j 1 R j Analyzing Circuits Tactics: • Replace each series & parallel part by their single component equivalence. • Repeat. Example 25.3. Series & Parallel Components Find the current through the 2- resistor in the circuit. Equivalent of parallel 2.0- & 4.0- resistors: 1 1 1 3 R 2.0 4.0 4.0 R 1.33 Equivalent of series 1.0-, 1.33- & 3.0- resistors: RT 1.0 1.33 3.0 5.33 Total current is I 5.33 12 V E RT 5.33 2.25 A Voltage across of parallel 2.0- & 4.0- resistors: V1.33 2.25 A1.33 2.99 V Current through the 2- resistor: I 2 2.99 V 2.0 1.5A 25.3. Kirchhoff’s Laws & Multiloop Circuits Kirchhoff’s loop law: V = 0 around any closed loop. ( energy is conserved ) Kirchhoff’s node law: This circuit can’t be analyzed using series and parallel combinations. I=0 at any node. ( charge is conserved ) Multiloop Circuits Problem Solving Strategy: INTERPRET ■ Identify circuit loops and nodes. ■ Label the currents at each node, assigning a direction to each. DEVELOP ■ Apply Kirchhoff ‘s node law to all but one nodes. ( Iin > 0, Iout < 0 ) ■ Apply Kirchhoff ‘s loop law all independent loops: Batteries: V > 0 going from to + terminal inside the battery. Resistors: V = I R going along +I. Some of the equations may be redundant. Example 25.4. Multiloop Circuit Find the current in R3 in the figure below. Node A: I1 I 2 I 3 0 Loop 1: E1 I1R1 I 3 R 3 0 6 2 I1 I 3 0 Loop 2: E2 I 2 R 2 I 3 R 3 0 9 4I2 I3 0 1 I1 I 3 3 2 I2 9 1 1 1 I 3 3 4 2 4 I3 4 21 3A 7 4 1 9 I3 4 4 Application: Cell Membrane Hodgkin-Huxley (1952) circuit model of cell membrane (Nobel prize, 1963): Resistance of cell membranes Membrane potential Electrochemical effects Time dependent effects 25.4. Electrical Measurements A voltmeter measures potential difference between its two terminals. Ideal voltmeter: no current drawn from circuit Rm = Example 25.5. Two Voltmeters You want to measure the voltage across the 40- resistor. What readings would an ideal voltmeter give? What readings would a voltmeter with a resistance of 1000 give? (a) (b) 40 V40 12 V 4 V 40 80 Rparallel 40 1000 40 1000 38.5 38.5 V40 12 V 3.95V 38.5 80 Ammeters An ammeter measures the current flowing through itself. Ideal voltmeter: no voltage drop across it Rm = 0 Ohmmeters & Multimeters An ohmmeter measures the resistance of a component. ( Done by an ammeter in series with a known voltage. ) Multimeter: combined volt-, am-, ohm- meter. 25.5. Capacitors in Circuits Voltage across a capacitor cannot change instantaneously. The RC Circuit: Charging C initially uncharged VC = 0 Switch closes at t = 0. VR (t = 0) = E I (t = 0) = E / R C charging: VR but rate I but rate VC but rate VC VR I Charging stops when I = 0. E I R dI dt I RC Q 0 C dI I R 0 dt C I dQ dt t dt dI I0 I 0 RC I VC ~ 2/3 E ln I t I0 RC I I0 e t RC VC E VR E RCt e R t E 1 e RC Time constant = RC I ~ 1/3 E/R The RC Circuit: Discharging C initially charged to VC = V0 Switch closes at t = 0. VR = VC = V I Q I R0 C dI dt I RC I I0 e t RC V V0 e V0 RCt e R t RC dQ dt I 0 = V0 / R C discharging: VC VR I Disharging stops when I = V = 0. Example 25.6. Camera Flash A camera flash gets its energy from a 150-F capacitor & requires 170 V to fire. If the capacitor is charged by a 200-V source through an 18-k resistor, how long must the photographer wait between flashes? Assume the capacitor is fully charged at each flash. V t RC ln 1 C E 170 V 18 103 150 106 F ln 1 200 V 5.1 s RC Circuits: Long- & Short- Term Behavior For t << RC: VC const, C replaced by short circuit if uncharged. C replaced by battery if charged. For t >> RC: IC 0, C replaced by open circuit. Example 25.7. Long & Short Times The capacitor in figure is initially uncharged. Find the current through R1 (a) the instant the switch is closed and (b) a long time after the switch is closed. (a) (b) I1 I1 E R1 E R1 R2