Current in an open RL circuit If the switch is thrown open after the current in an RL circuit has built up to its steady-state value I = V/R, the decaying current (see accompanying figure) obeys the equation di + Ri = 0, dt which is Equation (5) with V = 0. a. Solve the equation to express i as a function of t. b. How long after the switch is thrown will it take the current to fall to half its original value? c. Show that the value of the current when t = L/R is I/e. (The significance of this time is explained in the next exercise.) L. 1/2
Current in an open RL circuit If the switch is thrown open after the current in an RL circuit has built up to its steady-state value I = V/R, the decaying current (see accompanying figure) obeys the equation di + Ri = 0, dt which is Equation (5) with V = 0. a. Solve the equation to express i as a function of t. b. How long after the switch is thrown will it take the current to fall to half its original value? c. Show that the value of the current when t = L/R is I/e. (The significance of this time is explained in the next exercise.) L. 1/2
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Transcribed Image Text:Current in an open RL circuit If the switch is thrown open
after the current in an RL circuit has built up to its steady-state
value I = V/R, the decaying current (see accompanying figure)
obeys the equation
di
+ Ri = 0,
dt
which is Equation (5) with V = 0.
a. Solve the equation to express i as a function of t.
b. How long after the switch is thrown will it take the current to
fall to half its original value?
c. Show that the value of the current when t = L/R is I/e. (The
significance of this time is explained in the next exercise.)
L.
1/2
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