RL Circuits Physics 102 Professor Lee Carkner Lecture 21

PAL #21 Generator  To produce 12 amps in a 15 ohm wire you need an emf of  = IR = (12)(15) = 180 V  Set 180 V equal to the max emf   = NBA    =  /NBA = 180/(1)(2)(1) = 90 rad/s  If  = 90 rad/s, we can find f =  /2   f = 14.3 Hz or 14.3 cycles per second

Induction and Circuits   The changing magnetic field can then induce its own current that will oppose the initial changes  This means,   Note that induction only applies in circuits where the current changes  often this means a switch is closed or opened

Self Inductance   When the switch is closed, current flows through the loop, inducing a B field through the loop   Called self inductance

Back emf  The emf induced opposes the direction of the current change   Called the back emf   Current decreases, emf in same direction

Finding emf  The back emf depends on Faraday’s Law:  = -N(  /  t)   If we put the coil properties into the variable “L” we get:  = -L(  I/  t)   where the constant of proportionality L is the inductance  The unit of inductance is the Henry,  H (V s/A)

Inductance   = L(  I/  t) = N(  /  t) L = N(  /  I)  L =  0 n 2 Al  n=  A = cross sectional area  l = length

Inductors  In a circuit any element with a high inductance is represented by an inductor  Examples:  We will assume that the rest of the circuit has negligible inductance   Symbol is a spiral:

Magnetic Energy  A battery must do work to overcome the back emf of a circuit with inductance   Magnetic fields, like electric fields represent energy  Energy in an inductor is: E = (1/2) L I 2   B = (B 2 /2  0 )  This is how much energy per cubic meter is stored in a magnetic field B

Transforming Voltage   We often only have a single source of emf  e.g. household current at 120 V   We can use the fact that a voltage through a solenoid will induce a magnetic field, which can induce an emf in another solenoid

Basic Transformer

Transformer   The emf then only depends on the number of turns in each  = N(  /  t)  V p /V s = N p /N s  Where p and s are the primary and secondary solenoids   If N p > N s, voltage decreases (is stepped down)  If N s > N p voltage increases (is stepped up)

Transformers and Current  Energy is conserved in a transformer so:   V p /V s = I s /I p   Note that the flux must be changing, and thus the current must be changing  Transformers only work for AC current

Transformer Applications  Generators usually operate at ~10,000 volts   Since P = I 2 R a small current is best for transmission wires   Power pole transformers step the voltage down for household use to 120 or 240 V 

Next Time  Read  Homework, Ch 21, P 36, 43, 47, 53

A metal rod moves horizontally in a uniform vertical magnetic field. Which of the following changes would not increase the emf induced across the rod? A)Increasing the strength of the magnetic field B)Increasing the velocity of the rod C)Increasing the length of the rod D)Increasing the thickness of the rod E)Nothing can change the emf of the rod

Household electrical current has a frequency of 60 Hz. What is its angular frequency? A)9.5 rad/s B)60 rad/s C)188 rad/s D)377 rad/s E)600 rad/s

If the frequency of a generator is increased, A)The maximum emf goes up and the current changes direction more rapidly B)The maximum emf goes up and the current changes direction less rapidly C)The maximum emf goes down and the current changes direction more rapidly D)The maximum emf goes down and the current changes direction less rapidly E)The maximum emf does not change