PHYSICS Review for 2 nd exam. Exam format and rules. Closed book, ! Cheat sheet from me Need calculator No cell phones or computers Two sections Multiple choice / short answer Problems Remember Vectors need direction and magnitude All answers need units Significant figures count.
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Exam format and rules • Closed book, ! Cheat sheet from me • Need calculator • No cell phones or computers • Two sections • Multiple choice / short answer • Problems • Remember • Vectors need direction and magnitude • All answers need units • Significant figures count
Summary of Material in 2nd Test • Ch 25:Current, Resistance and EMF • Current, resistivity and resistance • Real and ideal batteries • Power in circuits and resistors • Ch 26: DC Circuits • Adding resistors and equivalent resistance • Loop Equations and multi-loop circuits • RC Circuits • Ch 27: Magnetic Fields and Forces • Force on a charged particle and current • Torque on a loop • DC motor and Hall effect • Ch 28: Sources of Magnetic Fields • Magnetic field of a moving charge or current • Ampere’s Law, Biot-Savart Law • Field due to a wire • Forces between wires • Ch 29: Induction • Faraday;s Law • Lenz Law Test will try to be approx. 50% circuits and 50% magnetic fields/induction
Circuits Section CH 25 - 26
A few things you have to know • What is current • What is a resistor • What is a voltage source • Unit of voltage • Relationship to energy and power • Ohm’s Law • Resistors in parallel and series
A few things you have to know • Circuit analysis through element reduction • How does an incandesant light bulb work • Kirkhoff’s laws and loop equations • Difference between real and ideal batteries • RC circuit • Time constant • Current and Charge as a function of time
A few things you don’t have to know • Cramer’s Rule
Current: CHARGES DRIFTING IN A CONDUCTOR Current Movement of charge I = dQ/dt Unit: Amp (C/s) Assumes (+) charge Not a vector! Current density J = Current/area
Resistance and Resistivity • Resistance is the property of a material to “slow down” current • Resistivity is a material property that how well a material conducts electricity • = E/J (definition) • Resistance • R = L/A
Equivalent Resistance Series connection Same current in each element Same Voltage in each element Parallel connection
Ohm’s Law We can write Ohm’s Law two ways • Microscopic • E = J • Macroscopic • V = IR
Practice :#1 A network consists of 10 identical resistors in parallel. If another resistor is added in parallel the total resistance Goes up slightly Goes down slightly Stays the same
Practice : #2 A network consists of 10 identical resistors in parallel. The voltage across this section is constant. If another resistor is added in parallel the current through the entire network Goes up slightly Goes down slightly Stays the same
Electrical Power Battery delivery power to a circuit • P = IV (W) Resistors dissipate power from a circuit • P = I2R (W)
Source of EMF: A battery • EMF is the electro motive force (not a force) • It an energy per unit charge, a voltage • A battery is one source of EMF, it provides a a voltage difference across its poles • We will learn about other sources later • Any real battery has an internal resistance r which reduces the effective voltage • V = E – Ir • Has to be there, if not, shorted battery gives infinite current!
Real batteries When the external load is small compared to the internal resistance of the battery: • You can ignore the internal resistance of the battery • The effect of the internal resistance will be large • Not enough information
Shorts Charge flows through a light bulb. Suppose a wire is connected across the bulb as shown. When the wire is connected, 1. all the charge continues to flow through the bulb. 2. half the charge flows through the wire, the other half continues through the bulb. 3. all the charge flows through the wire. 4. none of the above
Light bulbs In the above circuit A,B,C,D are identical bulbs. Bulb B is: Brighter than Bulb A Less bright than Bulb A The same as Bulb A
Opens In the above circuit A,B,C,D are identical bulbs. Bulb C is removed, the brightness of bulb A Increases Decreases Does not change
Hints for element Reduction in Circuits • Reduce circuit on group at a time • Re-draw circuit with equivalent resistor each time • Can re-arrange resistors if confused • Be careful of short circuits • Parallel resistors often simpler to calculate as fractions • Once you have found total equivalent resistance find the total current • Go back through the reduction steps to get current and voltage for each element using: R’s in series has same current, R’s parallel has same voltage
Method #1 Assign current with direction to each resistor Write node equations to reduce the number of unknown currents Write loop equations Solve for currents Method #2 Assign current to each loop Write loop equations For resistors that share loops use net current Solve for currents Using Kirchhoff’s Rules Sign Rules: Resistors are voltage drop (-) when going with the direction of the current Batteries are positive when going in the direction they push current
Which to use: Reduction or Kirchhoff • Reduction • Simple circuits • Often single battery • Resistors can be reduced in pairs or groups • Loop equations • Always works but sometimes math is worse • Needed when resistors can not be reduced in pairs • Often needed in multiple battery situations
Loop Example V1= 12V R1 = 3.0 W R2 = 3.0 W V2= 6V R3 = 6.0 W Assuming clockwise currents for both loop the loop equations for the upper loop is 12 -3i1 – 3(i1+i2) – 6 = 0 12 -3i1 – 3(i1- i2) – 6 = 0 12 -3i1 – 3(i1+i2) + 6 = 0
RC Circuits • Loop equation gives • 0 = V - IR - q/C • Solve for I • I = V/R - q/RC • When q = 0, I = V/R • When charged q = CV so I = 0 • I = dq/dt so solve differential equation to get • q(t) = Q(1-e-t/RC) and I(t) = I0e-t/RC • RC is the time constant of the circuit Important
CHARGING A CAPACITOR:current vs time CHARGING A CAPACITOR:charge vs time
DISCHARGING A CAPACITOR:current vs time DISCHARGING A CAPACITOR:charge vs time
A few things you have to know • Magnetic field • Unit • Size on earth • Effect of magnetic field on charges and current carrying wires • Path of a free charge in a magnetic field • Magnetic moment • Torque on loop in B field • DC motor
A few things you have to know • Magnetic field due to a wire • Sketch field lines, calculate vector field • Superposition due to many wires • Wires interacting with a force • Ampere’s Law • Faraday’s law • Lenz’ law
A few things you don’t have to know • Biot-Sevart Law
Practice Section 1 An electron (negative charge) enters the classroom from the front blackboard. Assume the earth’s magnetic field is straight down into the ground. Which way is the electron deflected? Toward the windows opposite the doors Toward the wall where the doors are Toward the floor Toward the back wall
I Force on a moving positive charge in a current-carrying conductor: L F = I L x B For vector direction use “RIGHT HAND RULE” I
Forces on the sides of a current-carrying loop in a uniform magnetic field.This is how a motor works!
Right hand rule determines the direction of the magnetic moment (m) of a current-carrying loop
Application: A simple DC motor t = m x B
A rectangular loop is placed in a uniform magnetic field with the plane of the loop perpendicular to the direction of the field. If a current is made to flow through the loop in the sense shown by the arrows, the field exerts on the loop: 1. a net force. 2. a net torque. 3. a net force and a net torque. 4. neither a net force nor a net torque.
A rectangular loop is placed in a uniform magnetic field with the plane of the loop parallel to the direction of the field. If a current is made to flow through the loop in the sense shown by the arrows, the field exerts on the loop: 1. a net force. 2. a net torque. 3. a net force and a net torque. 4. neither a net force nor a net torque.
If the Field is non-uniform you can cause a net force Current loops in a non-uniform B field
Chapter 28: Sources of Magnetic Fields • Biot-Sevart Law • Calculate Magnetic field from current elements • Ampere’s Law • Calculate Magnetic field from symmetry of the problem
Ampere’s Law • Allows us to use the symmetry of the situation to calculate the magnetic field • 4 Steps • Draw Amperian Loop • Direction matches right hand rule • Calculate the line integral around the loop • Calculate the enclosed current • Set current = integral and solve for B
Practice Section :#5 In a co-axial cable the inner conductor carries a current I, while the outer conductor carries a current –I. The magnetic field outside the outer conductor is: m0I/2pr 2 moI/2pr 0
Faraday’s Law of Induction How electric generators, credit card readers, and transformers work. A changing magnetic flux causes (induces) an emf in a conducting loop. C 2004 Pearson Education / Addison Wesley