RL Circuits Physics 102 Professor Lee Carkner Lecture 22

PAL #21 Generator  To produce 12 amps in a 15 ohm wire you need an emf of  = IR = (12)(15) = 180 V    = NBA    =  /NBA = 180/(1)(2)(1) =  If  = 90 rad/s, we can find f =  /2   f =

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

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 increases,  Current decreases,

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)  The induced emf is proportional to the rate of change of the current:   The unit of inductance is the Henry,  H (V s/A)

Inductance   = L(  I/  t) = N(  /  t) L = N(  /  I)  If we use a solenoid to create inductance, then L can be written as: L =  0 n 2 Al  n=  A =  l =

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

Today’s PAL  A solenoid that is 5 cm long and 1 cm in diameter is placed in a circuit. If 0.1 V of emf is induced by increasing the current from 0 to 3 A in 0.5 seconds, how many turns does the solenoid have?

Magnetic Energy   Can think of this energy as being stored in the magnetic field   Energy in an inductor is:  If we use the expression for L and B for a solenoid we can get the magnetic energy density,  B  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.  We need a device to transform the voltage  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  If we connect the two solenoids with a iron core, they will each have the same flux   = 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