To understand the behavior of an inductor in a series R-L circuit. In a circuit

Question

To understand the behavior of an inductor in a series R-L circuit. In a circuit containing only resistors, the basic (though lot necessarily explicit) assumption is that the current middot eaches its steady-state value instantly. This is not the Just as in the case of R-C circuits, the steady state here is never actually reached: The exponential functions approach their limits asymptotically as t oo. However, it usually does not take very long for the value of i to get very close to its presumed limiting value. The next several questions illustrate this point. Note that the quantity L/R has dimensions of time and is called the time constant (you may recall similar terminology applied to R-C circuits). The time constant is often denoted by r. Using r, one can write the expression Express your answer numerically, using three significant figures.

Explanation / Answer

       L- R CIRCUIT

   variation of current as a function of time is given by   

   i(t) = e/R (1- e^-(Rt/L))
= e/R (1-e^(-t/T)) ,T = L/R time constant of LR circuit,

current at t= 6T , is i(6T) = e/R(1- e^-(6T/T))

           i(6T) = e/R( 1- e^-6) -------------->(1)

the maximum current I max = e/R --------------->(2)

ratio (1)/(2) = e/R( 1- e^-6) / (e/R)

= ( 1- e^-6)
= 0.99752

ratio of currents at i(6T) to maximum current is = 0.99752

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