# Electric Circuit Theory. Applied Electricity and Electronics by R. Yorke

By R. Yorke

This revised and enlarged version offers a concise and entire advent to uncomplicated suggestions commonly used within the fields of electric, digital and keep an eye on engineering and communications. The textual content offers a lucid therapy of strategies and concept, which, supported by way of 250 labored difficulties and issues of solutions, makes the quantity a useful educating reduction for the lecturer and an invaluable textual content for self college through the scholar. This revised and enlarged variation features a new bankruptcy on two-port networks, extending the usefulness of the quantity in all undergraduate electric and digital engineering classes.

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N o t e that / is a constant equal to the current at t = 0, or / = i(0). 1) i(t) = Ie flows through a circuit consisting of resistance R and inductance L connected in series. D e t e r m i n e the voltage across the circuit. T h e circuit diagram and current waveform are shown in Fig. 2 . 1 . 1) into v(t)=Ri(t) st +L ^ - , st st u ( 0 = RIe + sLIe = I(R + sL) e . 3) is clearly of the form: v(t) = Ve\ where V = I(R + sL). 4). It is shown FIG. 2 . 1 . Circuit and current and voltage waveforms for Problem 2 .

18. FIG. 18. Inductors in series and parallel. ELECTRIC CIRCUIT THEORY 34 Solution Let the equivalent inductance be Le. —— • dt. • But, 17(0= 01 ( 0 + «fe (0> by Kirchhoff s second Law. Now, v2(t) dii(t) or dt i2(t) L2 Similarly, o2(t) h(t) dt, and i,(0 = » 2(0 + *3(0 by Kirchhoff's Law v2(t)dt _L2 + L3 v2(t) LL . dt. 23 Thus, v2(t) •• L2L3 VL2 + L, diiW dt Also "i ( 0 U diifrt dt i>2(t)dt. FIELDS, CIRCUITS AND CIRCUIT PARAMETERS 35 Hence, v(t) dii(t) dt VL 2+ L 3 L 2L 3 l d / , ( 0 L2 + L 31 dt dt dt Thus, L2 + L3 Hence, inductances combine as resistances do, viz.

2. Plot of Z(s) vs. s for /? and L in series. A case of special interest occurs when the graph of Z{s) crosses the axis of s. 6) s = ~ This is called a Z E R O of the impedance function. W h e n Z(s) = ± o o (in this case when s = ±<») this is called a POLE of the impedance function. T h u s , t h e function Z(s) = R + sL has o n e zero and o n e pole (±oo are counted as the same point). T h e impedance function is o n e example of a general network function. A n o t h e r is the admittance function which is defined as the reciprocal of Z ( s ) , and is denoted by Y(s).