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Homework Statement
At t = 0, a battery is connected to a series arrangement of a resistor and an inductor. If the inductive time constant is 42.1 ms, at what time (in ms) is the rate at which energy is dissipated in the resistor equal to the rate at which energy is stored in the inductor's magnetic field?
Homework Equations
power dissapated by resistor: P=(I^2)R
Power stored by inductor: P=IL(di/dt)
Current in an RL cuircuit: I=V/R(1-exp(-t/T))
where T is the time constant tau = (L/R)
The Attempt at a Solution
I just set them equal, then simplified.
(I^2)R = IL(di/dt)
I=(L/R)(di/dt)
replace L/R with Tau and Current with above equation
V/R(1-exp(-t/T)) = T (di/dt)
take derivative of current
V/R(1-exp(-t/T)) = T (V/R)(1/T)*exp(-t/T)
cancelations
1-exp(-t/T)=exp(-t/T)
add exp(-t/T) to both sides and take natural logs
Ln(1/2) = -t/T
so t = -T*Ln(1/2)
I plug this into the online homework and it keeps telling me I'm wrong, but I can't see
what I'm doing incorrectly, any ideas?
(sorry I don't know LaTex yet :P)
Homework Statement
Homework Equations
The Attempt at a Solution
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