Physics 1402: Lecture 10 Today s Agenda Announcements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW assignments, solutions etc. Homework #3: On Masterphysics : due Friday at 8:00 AM Go to masteringphysics.com Electromotive force Provides a constant potential difference between 2 points ε ε: electromotive force (emf) + May have an internal resistance - Not ideal (or perfect: small loss of ) Parameterized with internal resistance r in series with ε Potential change in a circuit ε - r - = 0 r ε 1
Power Batteries & esistors Energy expended chemical to electrical to heat ate is: What s happening? Charges per time Assert: Energy drop per charge For esistors: Batteries (non-ideal) Parameterized with internal resistance r in series with ε ε: electromotive force (emf) = (=0) ε - r = ε - r - = 0 r ε Power delivered to the resistor : P max when /r =1! 2
Conductors: Devices Purpose is to provide zero potential difference between 2 points.» Electric field is never exactly zero.. All conductors have some resistivity.» n ordinary circuits the conductors are chosen so that their resistance is negligible. Batteries (oltage sources, seats of emf): Purpose is to provide a constant potential difference between 2 points.» Cannot calculate the potential difference from first principles.. electrical chemical energy conversion. Non-ideal batteries will be dealt with in terms of an "internal resistance". + - O + - 3
esistors: Devices Purpose is to limit current drawn in a circuit.» esistance can be calculated from knowledge of the geometry of the resistor AND the resistivity of the material out of which it is made.» The effective resistance of series and parallel combinations of resistors will be calculated using the concepts of potential difference and current conservation (Kirchoff s Laws). esistance esistance is defined to be the ratio of the applied voltage to the current passing through. UNT: OHM = Ω How resistance is calculated esistivity property of all materials measures how much current density j results from a given electric field E in that material units are Ohm x m (Ω m) Conductivity sometimes used instead of resistivity measures the same thing as ρ esistance property of an object depends on resistivity of its material and its geometry Conductance sometimes used instead of resistance measures the same thing as 4
The oltage drops : esistors in Series 1 a b 2 Whenever devices are in SEES, the current is the same through both! This reduces the circuit to: a effective c Hence: c Another (intuitive) way... Consider two cylindrical resistors with lengths L 1 and L 2 1 L 1 L 2 2 Put them together, end to end to make a longer one... 5
What to do? esistors in Parallel ery generally, devices in parallel have the same voltage drop But current through 1 is not! Call it 1. Similarly, 2 2. How is related to 1 & 2?? Current is conserved! a d a d 1 2 1 2 Another (intuitive) way... Consider two cylindrical resistors with cross-sectional areas A 1 and A 2 A 1 A 2 1 2 Put them together, side by side to make a fatter one with A=A 1 +A 2, 6
esistors in series the current is the same in both 1 and 2 the voltage drops add Summary 1 esistors in parallel the voltage drop is the same in both 1 and 2 the currents add 2 1 2 Lecture 10, ACT 1 have two identical light bulbs. First hook them up in series. Then hook them up in parallel. n which case are the bulbs brighter? (The resistors represent light bulbs whose brightness is proportional to P = 2 through the resistor.) A) Series B) Parallel C) The same 7
ε 1 3 1 ε 2 2 ε 3 Kirchoff's First ule "Loop ule" or Kirchoff s oltage Law (KL) "When any closed circuit loop is traversed, the algebraic sum of the changes in potential must equal zero." KL: This is just a restatement of what you already know: that the potential difference is independent of path! ULES OF THE OAD: We will follow the convention that voltage gains enter with a + sign and voltage drops enter with a - sign in this equation. Move clockwise around circuit: ε 1 1 2 ε 2 ε 1 1 2 ε 2 = 0 8
Loop Example b 1 a ε 1 f 4 c d e 2 ε 2 3 KL: Lecture 10, ACT 2 Consider the circuit shown. The switch is initially open and the current flowing through the bottom resistor is 0. After the switch is closed, the current flowing through the bottom resistor is 1. What is the relation between 0 and 1? 12 12 12 (a) 1 < 0 (b) 1 = 0 (c) 1 > 0 9
Kirchoff's Second ule "Junction ule" or Kirchoff s Current Law (KCL) n deriving the formula for the equivalent resistance of 2 resistors in parallel, we applied Kirchoff's Second ule (the junction rule). "At any junction point in a circuit where the current can divide (also called a node), the sum of the currents into the node must equal the sum of the currents out of the node." This is just a statement of the conservation of charge at any given node. 10