Transcript Slide 1
Arrange the following in the order of current, starting with the lowest. (A) 7 coulombs in 3 seconds. (B) 10 Volts across 5 Ohms (C) 15 Volts across 7 Ohms (D) 2 Amps Question If a laptop needs constantly needs 2 Amps current from a battery, how many electrons are drained from the battery in one hour? 1 Amp = 6.242 x 1018 electrons/second 2 Amp = 12.484 x 1018 electrons/second In one hour - > 3600 x 12.484 x 1018 electrons Answer is 4.49 x 1022 electrons DC Voltage Supply Resistance R = ρ L/A ρ is the resistivity of the material (units?) Material ρ (10-8 Ohm-Metres) Silver Copper 1.645 1.723 Gold Aluminum Tungsten 2.443 2.825 5.485 Nickel Iron Tantalum Nichrome Tin Oxide Carbon 7.811 12.299 15.54 99.72 250 3500 American Wire Gage (AWG) sizes AWG # Diameter (in) Ω /1000ft. 0000 0.46 0.0490 000 0.409 0.0618 0 0.325 0.0983 1 0.289 0.1240 2 0.257 0.1563 4 0.204 0.2485 10 0.102 0.9989 14 0.0640 2.525 28 0.0126 64.90 Color Coding 5 Bands of code (3 are mandatory) Bands 1 - 3 the value of the resistor Band 4 the range (tolerance) Band 5 the reliability Color Code (Band 1-3) Color Value Black 0 Brown 1 Red 2 Orange 3 Yellow 4 Green 5 Blue 6 Violet 7 Gray 8 White 9 Band 3 (special cases) Gold = 0.1 Red Blue Gold = 2.6 Ohm Silver = 0.01 Red Blue Silver = 0.26 Ohm More Bands Band 4 Tolerance Gold 5% Silver 10% None 20% Band 5 Reliability (after 1000 Hrs of use) Brown 1% Red 0.1% Orange 0.01% Yellow 0.001% Ohm’s Law I = V/R V=IR R=V/I Power Power dissipated by charge flowing through a resistor P = VI P = V2/R P = I 2R Energy Energy = Power x Time Battery Chemical Reactions to produce potential difference Alkaline and lithium-iodine primary cells Lead Acid secondary cell Nickel-Cadmium Secondary cell Nickel-Hydrogen and Nickel-Metal Hydride Secondary cells Solar Cells Power Supply Used very frequently in all devices. Transform the AC supply into a lower voltage Rectify it (?) Current Sources Supplies a fixed amount of current It is the dual of the battery In a battery voltage is constant, but current drains out Ammeters Device to measure current The wire in which current is to be measured is broken up, and are joined via an ammeter. What should be the resistance of the ammeter? Voltmeters Devices to measure voltage Connected in a parallel fashion across the device where there is a need to measure potential difference. What should be the resistance of a voltmeter? Ohmmeters Used to measure the resistance of a device. Connected across the two pins of a resistor Also used to check the continuity of networks. Wattmeters Used to measure the dissipation of power in a circuit element. Includes both an ammeter and a voltmeter. Displays the multiplication of both measurements. Fuses and Circuit Breakers The power supply to the homes is not ideal. If it goes above a specified level, it can burn the devices. May result in Fire or Smoke. Fuse wires melt if they experience a large current. In a breaker, a large current results in a large enough strength in an inbuilt electromagnet to draw the switch open Series Circuit Two elements are in series if They have only one terminal in common. The common point in the two elements is not connected to a third current carrying element. Resistance The resistance seen by the source R=R1+R2 The two circuits on the right are equivalent R1 R2 R1+R2 Voltage Drop? The current through each resistor is calculated by the Ohm’s law =V1/R1 Where V1 is the voltage across the resistor. =V/RT Where RT is the total resistance in the circuit. V1 = VxR1/RT Power? Power dissipated in each resistor = V12/R1 P1 = (V2/RT2)x R1 P1 Total power = V2/RT = P1 + P2 + … Kirchhoff’s Voltage Law The algebraic sum of the potential rises and drops around a closed loop is zero. KVL V + V1+V2 = 0 Can anyone prove this mathematically? R1 V1 V R2 V2 Voltage Divider Rule In a series circuit the voltage across the resistive elements will divide as the magnitude of the resistors Ground Terminal This is not a loop. Or is it? Ground terminal means that the two points are both connected to ground and are at a zero potential. So this is a loop. Internal Resistances Voltage and other sources have internal resistances, and they should be counted while solving circuits. Resistance R = ρ L/(A1+A2) Solving in terms of R1 and R2 gives 1/R = 1/R1 + 1/R2 The total value of the resistance is always smaller than the smallest resistance Kirchhoff’s Current Law KCL states that the algebraic sum of the currents entering and leaving a point or junction is zero. i1+i2+i3+i4=0 i1 i2 i3 i4 Current Divider Rule For parallel elements of different value the current will split with a ratio equal to the inverse of their resistor value Reduce and Return Approach Applicable to all single source circuits. Currents in Loops (Remember KCL?) i1 i2 i3 Ladder Networks There are 2 approaches to solve this circuit Reduce Resistances using series parallel analysis Calculate current using current loops No - Load When is “no load” observed? When large? Or when R2 is zero? R1 R2 R2 is infinitely When R2 is infinite!!! Voltage Divider Supply V1 R1 V2 R2 V3 R3 We cannot calculate V2 and V3 unless we know what load is connected to them The less the load, the closer they are to 9V. Potentiometer Voltage Sources Two voltage sources of different ratings may not be connected in parallel. Why? Series operation, however, is permitted. Current Sources Two current sources of different rating may not be connected in series. Parallel operation, however, is permitted.