Electric power

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Electric power [Copy link]

1. Power absorbed by a branch
Figure 1-5-1 shows a branch in a circuit (it can be an active branch or a passive branch). Assume that the reference direction of the branch current i and the reference polarity of the branch voltage u are the associated reference directions, as shown in the figure. The power absorbed by the branch at time t is defined as 　 p(t)=u(t)i(t). Since u and i are both algebraic quantities, p is also an algebraic quantity. If p>0 , the branch actually absorbs power; if p<0 , the branch actually emits power. 500)this.style.width=500;" border=0>

Figure 1-5-1 Branch power

2. Power generated by the power supply
Figure 1-5-2 (a) shows an ideal voltage source. Assume that the polarity of its voltage us and the reference direction of the terminal current i are as shown in the figure, that is, they are not related. Then the power generated by the ideal voltage source is 　ps=us i

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Figure 1-5-2 Power generated by power supply

Figure 1-5-2 (b) shows an ideal current source. Assume that the direction of its current is and the reference polarity of the terminal voltage u are as shown in the figure, that is, they are independent of each other . The power generated by the ideal current source is ps =isu. If ps _> 0 , the power supply actually emits power ; if ps <0 , the power supply actually absorbs power.

3. Power absorbed
by a resistor Figure 1-5-3 shows a resistor. Assuming voltage u and current i are related reference directions, the electric power it absorbs is:
p(t)=u(t)i(t)=R[i(t)] ² =[u(t)] ² /R
The energy absorbed by the resistor in the time interval (-∞, t) is:
w R (t)= 500)this.style.width=500;" align=absMiddle border=0>R[i(τ)] ² dτ= 500)this.style.width=500;" align=absMiddle border=0> {[u(τ)] ² /R}dτ

　

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Figure 1-5-3 Resistor circuit

The above two equations show that at any time t, the power p(t) and energy Wr(t) absorbed by the positive resistor are ≥ 0, and are converted into other forms of energy. This shows that the positive resistor element (R>0) is an energy-consuming element and a passive device.