Unformatted text preview: 246 Chapt. 32 Inductance and Inductors b) At what time (in numerals) does the current reach half its final value (i.e., half its value at time infinity)? 032 qfull 00420 3 3 0 tough math: solving a DE for an RL circuit 1 3. It’s about time youall solved a differential equation (DE). Consider the simple oneloop RL circuit DE with a constant driving emf E (i.e., an emf, resistor and inductor in series): LI ′ + IR = E . a) Draw a diagram of the circuit. b) It’s easier to solve a homogeneous DE than an inhomogeneous one. Differentiate the DE to get a DE for I ′ . c) Solve the DE of part (b) for the solution for I ′ and integrate it for the general solution for I . The solution should have two undetermined constants that set by boundary conditions of the problem. Define an efolding time (or time contant) τ to be used in simplifying the solution. d) What is the formula for the power outflow from the circuit to the inductor for the special case of our system. HINT: A negative power outflow is a power inflow.A negative power outflow is a power inflow....
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This note was uploaded on 11/16/2011 for the course PHY 2053 taught by Professor Buchler during the Fall '06 term at University of Florida.
 Fall '06
 Buchler
 Physics, Current, Inductance

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