RL Circuits Physics 102 Professor Lee Carkner Lecture 22

PAL #21 Generator   Set 180 V equal to the max emf   =   =  /NBA = 180/(1)(2)(1) = 90 rad/s  If  = 90 rad/s, we can find f =  /2   f =

Induction and Circuits   The changing magnetic field can then induce a current   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   Works like a battery that is put in “backwards”   Direction of emf depends on how current changes   Current increases, emf in reverse direction  Current decreases, emf in same direction

Inductance and Increasing Current

Effect of Back emf

Finding emf   emf depends on Faraday’s Law:   But the magnetic flux depends on the changing current and the properties of the coil   = -L(  I/  t)   where the constant of proportionality L is the inductance

Inductance  The unit of inductance is the henry,   The inductance of a circuit element (like a solenoid) depends on the current and the flux flowing through it  L = N(  /  I)   Inductance is a property of the circuit element  Like resistance

Solenoid Inductance  To find L, we need a relationship between  and I   What is (  /  I)?    = BA cos  or  = BA   B =  0 (N/l)I or I = Bl/(  0 N)   L = N(  /  I) = N  /I = NBA  0 N/Bl =  0 N 2 A/l L =  0 n 2 Al

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?

RL Circuits   As current tries to flow, it is resisted by the inductor   Time depends on R and L   Current can’t get to max value or 0 instantly

A RL Circuit

Time Constant  The characteristic time  is given as:   Larger inductance means longer delay  I = (  /R)[1 - e (-t/  ) ]   Note the similarities to a RC circuit

Current Rise with Time

Energy in an Inductor   This work can be thought of as energy stored in the inductor  E = (1/2) L I 2   E and I are the values for the circuit after a “long time” 

Magnetic Energy  Where is this energy stored?   Magnetic fields, like electric fields both represent energy   B = (B 2 /2  0 )  This is how much energy per cubic meter is stored in a magnetic field B

Transforming Voltage  It is important to provide an electrical device with the right voltage   We often only have a single source of emf    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   The ratio of emf’s is then just equal to the ratio of turns V p /V s = N p /N s   Device is called a transformer  If N p > N s, voltage decreases  If N s > N p voltage increases

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 

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