By J. David Irwin, R. Mark Nelms
Irwin's uncomplicated Engineering Circuit research has outfitted an excellent recognition for its hugely available presentation, transparent reasons, and broad array of worthy studying aids. Now in a brand new 8th variation, this hugely obtainable booklet has been fine-tuned and revised, making it better or even more straightforward to exploit. It covers such issues as resistive circuits, nodal and loop research thoughts, capacitance and inductance, AC steady-state research, polyphase circuits, the Laplace rework, two-port networks, and masses extra.
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Additional info for Basic Engineering Circuit Analysis, Problem Solving Companion
2(a) In the steady-state time interval prior to switch action, the inductor looks like a shortcircuit. Therefore, in this time period t < 0, the initial inductor current is iL(0-) = IS = 5mA At t = 0 the switch changes positions and hence for t > 0 the network reduces to that shown in Fig. 2(b). 55 i (t ) R 1 = 1k i = 1mH R 2 = 3k Fig. 2(b) If we let R = R1⎟ ⎜R2 then the differential equation for the inductor current is L di (t ) + R i (t ) = 0 dt The solution of this equation is of the form −t i (t ) = k 1 + k 2 e τ The differential equation has no constant forcing function and hence k1 = 0.
Recall, that in order to zero a voltage source, we replace it with a short circuit since the voltage across a short circuit is zero. In addition, in order to zero a current source, we replace the current source with an open circuit since there is no current in an open circuit. Consider now the voltage source acting alone. The network used to obtain this contribution to the output V0 is shown in Fig. 1(a). 8kΩ 6kΩ 12V + + V0 4kΩ 6mA - Fig. 1(a) Then V0 ′ (only a part of V0 ) is the contribution due to the 12V source.
2, find the waveform for the inductor current. 2 0 t(s) Fig. 3 Find the equivalent capacitance of the network in Fig. 3 at the terminals A-B. All capacitors are 6µF. A C eq B Fig. 4 Find the equivalent inductance of the network in Fig. 4 at the terminals A-B. All inductors are 12mH. 43 A B Fig. 1 The equations for the waveforms in the 4 two millisecond time intervals are listed below. v (t ) = mt + b 2 = t 2 × 10 −3 =2 2 = −2+ t 2 × 10 −3 4 = + 16 − t 2 × 10 −3 =0 0 ≤ t ≤ 2ms 2 ≤ t ≤ 4ms 4 ≤ t ≤ 6ms 6 ≤ t ≤ 8ms t < 0, t > 8ms Note that within each interval we have simply written the equation of a straight line using the expression y = mx + b or equivalently v(t) = mt + b where m is the slope of the line and b is the point at which the line intersects the v(t) axis.