DC circuits, Kirchhoff s Laws Alternating Current (AC), Direct Current (DC) DC Circuits Resistors Kirchhoff s Laws CHM6158C - Lecture 2 1
Electric current Movement of electrons in a conductor Examples of good conductors: copper aluminum silver Units: Cable enclosed with an insulating material (e.g. polyethylene) At what speed does electricity propagate? Charge (Q) Coulomb (C) 1.603x10-19 C Voltage (V) Volts (V) 1 V = 1 J/C Current (I) Amperes (A) 1 C/s Power (P) Watts (W) P = IV http://www.hydroquebec.com/learning/images/questceque/i_schema_atome.gif A current of 100 ma can be lethal! 2
Conduc@vity Conductivity = measure of a material s ability to conduct an electrical current silver > copper > aluminum Inverse: Resis@vity vs. Resistance Resistivity = measure of how strongly a material opposes the flow of electrical current (units: Ω m) (inherent of material) Strange units why? ρ = E J Magnitude of electric field (V / m) Magnitude of current density (A / m 2 ) Resistance = measure of how strongly a material opposes the flow of electrical current (units: Ω ) (dependent on cross-section and length of material) OHM s LAW R = V I 3
Alterna@ng current (AC) AC (alternating current): movement of electric charges periodically changes direction Mains power: 110 V RMS, 60 Hz Actually, this is the root-mean-square (RMS) voltage = V 0-p /sqrt(2) 4
Direct current (DC) Current flowing in one direction (typically static or changing slowly) Exact nature of voltage depends on power source 5
DC circuit Can think of this as movement of electrons from source potential to + around the circuit e.g. battery However, convention in electronics, current moves from + to in the circuit. This can be imagined as a movement of the charge as holes (i.e., absence of electrons), which is especially useful for semi-conductors (diodes, transistors). What will determine the amount of current that will move through the circuit for a given voltage? 6
Ohm s Law Convention: current flows from + to in the circuit What is voltage here? Voltage drop across the resistor e.g. +3 V and -3V What is the current in the circuit? What is voltage here? 7
Resistors: facts Made of a compound, film or resistance wire (e.g. nickel/chrome) Symbols: Important consideration: what is the maximum dissipative power (W) that a resistor can tolerate? P = IV = I*(IR) = I 2 R Resistors will burn out if the dissipative power is too great! 8
Resistor nota@on 4 bands: 5% accuracy 9
Kirchhoff s Laws 1. At any node in an electrical circuit, the sum of the currents flowing into that node is equal to the sum of the currents flowing out of that node. (= conservation of charge) I t I 1 For a parallel circuit of N resistors, the total current I into the junction equals the sum of currents (I 1 + I 2 + I 3 +. + I N = I total ) I 2 2. The directed sum of the electrical potential differences around a closed circuit is zero (= conservation of energy) For a series circuit of N resistors, the sum of the voltage drops (IR 1 + IR 2 + IR 3 +. + IR N = V source ) 10
Resistors in series Current is the same everywhere in the circuit. What can this principle be useful for? 1.5 V battery V in = IRtotal = IR1 + IR2 = 1 + R I( R ) 2 By analogy for N resistors in series: V in = IR total = IR1 + IR2 +... IR = ( N I N 1 R) 11
Resistors in parallel What will happen when one resistor has a much higher value than the other one? Voltage drop across each resistor identical, but current is depends on resistance R. In this case, total current = sum of currents I in = I 1 + I 2 Know that In general: V in = V 1 = V 2 N 1 1 = Rtotal 1 R i V R V R in 1 = + total 1 V R 2 2 12
Digital mul@meter (DMM) Can measure resistances, voltage and current (AC and DC). If measure voltage, what do we want internal resistance of the multimeter to be? If measure current, what do we want internal resistance of the multimeter to be?.. Why would you NEVER connect multimeter in current-reading mode to measure between 0 and +1.5 V? N. B. In Lab Unit 1, will become familiarized with measuring DC voltages. 13
Equivalent circuits 1 R 2,3 = 1 R 2? + 1 R 1 = 1 R 2,3 20 + 1 40 = 1 13.3! 3 I = V R total 15( V ) = 9? + 13.3( Ω) = 0.67( A) 14
Voltage divider In this case, would it be safe to measure the current between 0.8 V AB and 0.6 V AB for instance? What consequences would this have for the circuit? What would happen to the circuit if we measured the voltage between 0.8 V AB and 0.6 V AB? 15
What is the current in this circuit? Examples Assume all resistors are equivalent (100 Ω), what is the total resistance of these circuits? 16