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chp36_3 - PHY2061 R D Field RL Circuits"Building-Up Phase A...

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PHY2061 R. D. Field Department of Physics chp36_3.doc University of Florida RL Circuits "Building-Up" Phase: Connecting the switch to position A corresponds to the "building up" phase of an RL circuit . Summing all the potential changes in going around the loop gives ε = IR L dI dt 0 , where I(t) is a function of time. If the switch is closed ( position A ) at t=0 and I(0)=0 ( assuming the current is zero at t=0 ) then d I d t I R = − 1 τ ε , where I have define τ =L/R . Dividing by (I- ε /R) and multiplying by dt and integrating gives ( ) dI I R dt I t = − ε τ / 0 0 1 , which implies ln / / I R R t  = − ε ε τ . Solving for I(t) gives ( ) I t R e t ( ) / = ε τ 1 . The potential change across the inductor is
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