Page 20 - Schaum's Outline of Theory and Problems of Electric Circuits

CIRCUIT CONCEPTS
CHAP. 2]

Fig. 2-5 9

2.3 VOLTAGE-CURRENT RELATIONS
The passive circuit elements resistance R, inductance L, and capacitance C are defined by the
manner in which the voltage and current are related for the individual element. For example, if the
voltage v and current i for a single element are related by a constant, then the element is a resistance,
R is the constant of proportionality, and v ¼ Ri. Similarly, if the voltage is the time derivative of the
current, then the element is an inductance, L is the constant of proportionality, and v ¼ Ldi=dt.
Finally, if the current in the element is the time derivative of the voltage, then the element is a
capacitance, C is the constant of proportionality, and i ¼ Cdv=dt. Table 2-1 summarizes these rela-
tionships for the three passive circuit elements. Note the current directions and the corresponding
polarity of the voltages.

Table 2-1
Circuit element Units Voltage Current Power

v 2
ohms (
) v ¼ Ri i ¼ p ¼ vi ¼ i R
(Ohms’s law) R

Resistance

ð
di 1 di
henries (H) v ¼ L i ¼ vdt þ k 1 p ¼ vi ¼ Li
dt L dt

Inductance

ð
1 dv dv
farads (F) v ¼ idt þ k 2 i ¼ C p ¼ vi ¼ Cv
C dt dt

Capacitance