P31_061 - P = i 2 R = i 2 Re 2 t/ L . Over a long time...

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61. Suppose that the switch had been in position a for a long time so that the current had reached the steady-state value i 0 . The energy stored in the inductor is U B = 1 2 Li 2 0 . Now, the switch is thrown to position b at time t = 0. Thereafter the current is given by i = i 0 e t/τ L , where τ L is the inductive time constant, given by τ L = L/R . The rate at which thermal energy is generated in the resistor is given by
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Unformatted text preview: P = i 2 R = i 2 Re 2 t/ L . Over a long time period the energy dissipated is Z P dt = i 2 R Z e 2 t/ L dt = 1 2 i 2 R L e 2 t/ L = 1 2 i 2 R L . Upon substitution of L = L/R this becomes 1 2 Li 2 , the same as the total energy originally stored in the inductor....
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