3.3. Power and energy Power is the rate of energy expenditure given as:
p =
dW dt =
dW dq dq dt =ui =i 2
R Where, the letter,
p , is power measured in watts(W), and the letter,
w , is energy measured in
joules(J). Power is usually determined by the product of voltage across a circuit element and
the current through it. By convention, we assume that a positive value for power indicates that
power is being delivered (or absorbed or consumed) by the circuit element. A negative value
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for power indicates that power is being extracted or generated by the circuit element which
could be considered as a battery.
Figure 22. Polarity references for four cases of current and voltage. Cases (a) and (d) result in positive power being
consumed by the circuit element. Cases (b) and(c) result in negative power being extracted from the circuit element.
Figure 22 illustrates the four possible cases for a circuit element’s voltage and current config‐
uration. According to the convention, if current and voltage are positive, with the arrow and
polarity shown in figure 22, energy is absorbed. If either the current arrow or the voltage
polarity is reserved, as in (b) and (c), energy is supplied to the circuit. If both the current
direction and voltage polarity are reserved together as in figure 22(d), energy is absorbed.
Figure 23. Basic symbol for independent source
A passive circuit element is defined as an element whose power is always positive or zero,
which is dissipated as heat (resistance), stored in an electric field (capacitor), or stored in
magnetic field (inductor). We define an active circuit element as one whose power is negative
and capable of generating energy. Energy is given by the following equation:
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W =
∫ −∞ t pdt In circuit, the basic source symbol is listed in figure 23.