RL Circuits PH 203 Professor Lee Carkner Lecture 21

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

RL Circuits  What happen when you have a resistor and an inductor in a circuit and you switch on a battery?   It takes time for the current to reach its full value   Inductors cause delays in current  Current can’t get to max value or 0 instantly

Time Constant  The characteristic time  is given as:  = L/R   Smaller resistance means more current and thus more inductance and thus longer delay   Current reaches max value at about 4   Note the similarities to a RC circuit

Rise of Current   After a long enough time the current reaches its maximum value =  /R  i = (  /R)[1 - e (-t/  ) ]  Note that current rises rapidly at first and then more slowly approaches max i

Current Rise with Time

Fall of Current   After a long enough time it becomes zero  i = (  /R)[e (-t/  ) ]  Both rise and fall are exponential

Inductor Tips  Current is time dependant   Inductors act like batteries   Need  battery and  inductor terms   At t>>4 ,  inductor = 0

Energy in an Inductor   This work can be thought of as energy stored in the inductor  U = (1/2) L i 2  Note that i and thus U vary with time   Note similarities to a capacitor

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

Next Time  Read  Problems: Ch 30, P: 44, 54, 64, Ch 31, P: 1, 9