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RL Circuits PH 203 Professor Lee Carkner Lecture 21

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

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

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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

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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

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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

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Current Rise with Time

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

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

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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

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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

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Next Time Read 31.1-31.5 Problems: Ch 30, P: 44, 54, 64, Ch 31, P: 1, 9

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