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| learn:courses:real-analog-chapter-1:start [2017/04/18 20:47] – [Passive Sign Convention] Martha | learn:courses:real-analog-chapter-1:start [2022/10/04 11:38] (current) – external edit 127.0.0.1 | ||
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| ====== 1. Introduction and Chapter Objectives ====== | ====== 1. Introduction and Chapter Objectives ====== | ||
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| Mathematically, | Mathematically, | ||
| - | $$ i=\frac{dq}{dw}\ (Eq. 1.2) $$ | + | $$ i=\frac{dq}{dt}\ (Eq. 1.2) $$ |
| Where //i// is the current in amperes, //q// is the charge in coulombs, and //t// is the time in seconds. Thus, current is the time rate of change of charge and units of charge are coulombs per second, or //amperes// (abbreviated as // | Where //i// is the current in amperes, //q// is the charge in coulombs, and //t// is the time in seconds. Thus, current is the time rate of change of charge and units of charge are coulombs per second, or //amperes// (abbreviated as // | ||
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| === Example 1.5: === | === Example 1.5: === | ||
| - | In Fig. (a) below, the element agrees with the passive sign convention since a positive current is entering the positive voltage node. Thus, the element of Fig. (a) is absorbing energy. In Fig. (b), the element is absorbing power - positive current is leaving the negative voltage node, which implies that positive current enters the positive voltage node. The element of Fig. (c) generates power; negative current enters the positive voltage node, which disagrees with the passive sign convention. Fig. (d) also illustrates an element which is generating power, since positive current is entering a negative voltage node. | + | In Fig. (a) below, the element agrees with the passive sign convention since a positive current is entering the positive voltage node. Thus, the element of Fig. (a) is absorbing energy. In Fig. (b), the element is absorbing power - positive current is leaving the negative voltage node, which implies that positive current enters the positive voltage node. The element of Fig. ( c) generates power; negative current enters the positive voltage node, which disagrees with the passive sign convention. Fig. (d) also illustrates an element which is generating power, since positive current is entering a negative voltage node. |
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| **Note:** | **Note:** | ||
| - | For the most part, we will consider only linear resistors in this text. These resistors obey the linear voltage-current relationship shown in equation (1.5). All real resistors are nonlinear to some extent, but can often be assumed to operate as linear resistors over some reange | + | For the most part, we will consider only linear resistors in this text. These resistors obey the linear voltage-current relationship shown in equation (1.5). All real resistors are nonlinear to some extent, but can often be assumed to operate as linear resistors over some range of voltages and currents. |
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| ==== Conductance ==== | ==== Conductance ==== | ||
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| $$ G=\frac{1}{R} | $$ G=\frac{1}{R} | ||
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