Question

the value of resistor is 1k

Consider the circuit shown in the f is no initial energy stored in the circuit, and the switch Si closed at time to. A. Find the time constant, t. B. What is the final (steady-state ) current in the circuit C. Find the time it takes for the current (lu) to reach 90% of its final value If the initial current in the inductor equal lo=-15 mA, D. Find the exponintial function that descripe Vi) for t>0 E. Plot Ih(t) versus t for t>0

Answer 1

Time constant = tau = L/R = 100 mH/1 K = 100 times 10^-3 times 10^-3 s = 1-^-4 s in steady state, inductor acts as a short circuit so, Current at steady state = 15 V/1 k ohm = 15 mA initial Current = I(0^-) = 0 A final current = I(infinity) = 15 mA time constant = z = 10^-4 s so, current equation is I(t) = 15(1 - e^-t/10^-4 mA 90% of 15 mA = 15 times 0.9 = 13.5 so, 13.5 = 15(1 - e^-t/10^-4) e^-t/10^-4 = 0.1 -t/10^-4 = log_e(0.1) = -2.3 t = 2.3 times 10^-4 so, it takes, 2.3 times 10^-4 s to reach the current to 90% of its final value.