SUMMARY

Monday, 10 September 2018

12:11 PM

Machine generated alternative text: • • • • An inductor is a circuit element that stores energy in its magnetic field. Inductance L is the property of inductors by which they oppose to changes in the current flowing through them. It is measured in henry (H). Voltage in an inductor is proportional to the time rate of change of its current. di dt i(t) ¯ — + i(to) to Energy stored in an inductor is proportional to the square of its current. 1 = -Li2 2 Inductor acts as a short circuit to DC voltage. Series combination of inductors is similar to series resistors. Parallel combination of inductors is similar to parallel resistors. 1 1 1 Leq - Ll L2 1

 

Machine generated alternative text: • Natural response of RL circuits Behaviour of the circuit (in terms of voltage or current) due to initial energy stored. — If the inductor has an initial current i(0) = 10, the natural response of the RL circuit is: i(t) = 10 e — The natural response decays to zero exponentially. — The speed at which the current decays is given by the time constant: • Time constant is the time required for the response to decay to a factor of l/e or 36.8% of its initial value or to reach 63.2% of its final value. For an RL circuit T = The resistance for the time constant is the Thevenin equivalent resistance as seen from the inductor terminals. After 5 time constant, 5T, the inductor current is considered to have reached its final value.

 

Machine generated alternative text: • Step response of RL circuits The unit step function can be used in electric circuits to model switching. u(t) = The step response is the response to a sudden change in the input sources. The inductor current over time is obtained as an exponential function: vs — If the initial current i(0) = 0 A, the response is known as forced response. The step response with non-zero initial condition is known as complete response. • It can be described as the sum of transient and steady state responses. — The solution to the step response of RL circuits can be given as follows: i(t) = i(oo) + [i(O) — t > O i(0): Initial current at t = 0. i(oo): Final or steady-state value at t -9 co. : Time constant at t -9 00. RTh co

 

 

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