- #1
Joseph M. Zias
- 78
- 28
For reference: Engineering Circuit Analysis, Hayt & Kemmerly, 4th ed, 1986, page 345.
Given a series RL circuit, the phasor current is I(s) = Vm/(R+sigma L), where S = sigma, w (omega) = 0. Thus we are dealing with only a exponential forcing function. Obviously I(s) goes to zero as sigma approaches infinity.
However, apply an exponential forcing function of Vm e^sigma t. t = time. Assuming we allow the transient to decay and then just look at the forced function we have: i(t) = (Vm/(R + sigma L) ) x e^sigma t.
Now, my question:
given some time longer than transient does the current i(t) approach infinity as sigma approaches infinity since e^sigma outranks sigma (basic limits). This essentially is questioning looking at only the phasor current.
Given a series RL circuit, the phasor current is I(s) = Vm/(R+sigma L), where S = sigma, w (omega) = 0. Thus we are dealing with only a exponential forcing function. Obviously I(s) goes to zero as sigma approaches infinity.
However, apply an exponential forcing function of Vm e^sigma t. t = time. Assuming we allow the transient to decay and then just look at the forced function we have: i(t) = (Vm/(R + sigma L) ) x e^sigma t.
Now, my question:
given some time longer than transient does the current i(t) approach infinity as sigma approaches infinity since e^sigma outranks sigma (basic limits). This essentially is questioning looking at only the phasor current.
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