A 20-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1 henry and the resistance is 50 ohms. Find the current i(t) if i(0) = 0.
i(t = _____
Determine the current as t → ∞.
lim i(t) =
t→∞
1
Expert's answer
2020-06-24T17:58:30-0400
For a series circuit containing only a resistor and an inductorKirchhoff’s second law states that the sum of the voltage drop across the inductor Ldtdi and the voltage drop across the resistor(iR) is the same as the impressed voltage on the circuit E(t)Ldtdi+Ri=E(t)∵L=0.1H and R=50Ω and E=20V∴0.1dtdi+50i=20∴dtdi+500i=200 linear differential Equation The integrating factor ise∫500dt=e500t∴ie500t=∫200e500tdt=52e500t+c∴i(t)=52+ce−500t Applying the initial condition i(0)=0 0=52+ce0→c=−52 Substitute in i(t)∴ The current i(t) if i(0) = 0 is i(t)=52−52e−500t(1)∴limt→∞i(t)=limt→∞(52−52e−500t)=52−52(0)=52(2)
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