Consider the circuit. Suppose that the switch S has been closedfor a very long t
ID: 1723400 • Letter: C
Question
Consider the circuit. Suppose that the switch S has been closedfor a very long time when you connect a wire across the battery, asshown in the figure on the right.
a. What is the magnitude of thecurrent through the inductor the instant after you connect thewire?
b. Is the magnitude of the current constant, increasing or decreasingas a function of time?
c. What is the time constantfor this circuit>
d. What will be the magnitude of the current in the circuit timeseconds after you close the switch?
Explanation / Answer
Current through RL circuit is I = I0* (1 - e-Rt/L) = (V/R)* (1 - e-Rt/L) a. at the time ofcontact t = 0 => I = (12/45)* ( 1 - e-45 * 0 /0.5) = 0 A b. The magnitude of currentwill increase with time asymptotically towards maximum value ofI0 . c. Timeconstant = L/R = 500 * 10-3 /45 = 11.11 *10-3 s = 11.11 ms d. After longtime, I = I0 asthe exponential will reduce to very very samll value I = I0 = V/R = 12/45 = 0.267 A a. at the time ofcontact t = 0 => I = (12/45)* ( 1 - e-45 * 0 /0.5) = 0 A b. The magnitude of currentwill increase with time asymptotically towards maximum value ofI0 . c. Timeconstant = L/R = 500 * 10-3 /45 = 11.11 *10-3 s = 11.11 ms d. After longtime, I = I0 asthe exponential will reduce to very very samll value I = I0 = V/R = 12/45 = 0.267 A