6.7 Summary

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6.7 Summary

1. The current through a capacitor is directly proportional to the time rate of change of the voltage across it.

$$i = C \frac{dv}{dt}$$

The current through a capacitor is zero unless the v oltage is changing. Thus, a capacitor acts like an open circuit to a dc source.

2. The voltage across a capacitor is directly proportional to the time integral of the current through it.

$$v = \frac{1}{C} \int_{-\infty}^{t} i \, d\tau = \frac{1}{C} \int_{t_0}^{t} i \, d\tau + v(t_0)$$

The voltage across a capacitor cannot change instantly.

• 3. Capacitors in series and in parallel are combined in the same w ay as conductances.
• 4. The voltage across an inductor is directly proportional to the time rate of change of the current through it.

$$v = L\frac{di}{dt}$$

The voltage across the inductor is zero unless the current is chang ing. Thus, an inductor acts like a short circuit to a dc source.

5. The current through an inductor is directly proportional to the time integral of the voltage across it.

$$i = \frac{1}{L} \int_{-\infty}^{t} v \, d\tau = \frac{1}{L} \int_{t_0}^{t} v \, d\tau + i(t_0)$$

The current through an inductor cannot change instantly.

• 6. Inductors in series and in parallel are combined in the same w ay resistors in series and in parallel are combined.
• 7. At any given time t, the energy stored in a capacitor is _1 ^{2 C}v² , while the energy stored in an inductor is _1 ² Li² .
• 8. Three application circuits, the inte grator, the differentiator, and the analog computer , can be realized using resistors, capacitors, and op amps.