RC时间常数为什么单位是s?

lukeluck

今天看了老外的分析，豁然开朗。

At first glance, this would seem to be very strange. How can the product of a resistance in ohms and a capacitance in farads possibly give us a time in seconds? To understand how this is possible, we go back to the basic definitions and some dimensional analysis.

3 s% [' }5 V/ o5 b" nResistance
Resistance opposes the flow of current through a circuit. By Ohm's Law, R = E/I. Thus, 1 ohm may also be expressed as 1 volt/ampere.
Current
Current is a measure of the amount of charge flowing through a circuit in a given amount of time. By primary definition, 1 ampere is equal to 1 coulomb/second.
Capacitance
Capacitance is the capacity to hold an electrical charge. A capacitance of 1 farad will exhibit a change of 1 volt if 1 coulomb of charge is moved from one plate to the other. Hence, 1 farad can be expressed as 1 coulomb/volt.

Putting these three basic definitions together we get the following progression:

RC	=	ohms	×	farads
	4 B3 r; d% l; p0 ~" m
	=	volts	×	coulombs
		amperes		volts
	=	volts	×	coulombs
		coulombs/seconds		volts
	=	volts × seconds	×	coulombs
		coulombs		volts
	=	seconds

Thus, we see that the RC product is indeed a measure of time, and can properly be described as the time constant of this circuit. This in turn means that this curve can be used to determine the voltage to which any capacitor will charge through any resistance, over any period of time, towards any source voltage. It is the general curve describing the voltage across a charging capacitor, over time.

Theoretically, C will never fully charge to the source voltage, E. In the first time constant, C charges to 63.2% of the source voltage. During the second time constant, C charges to 86.5% of the source voltage, which is also 63.2% of the remaining voltage difference between E and vC. This continues indefinitely, with vC continually approaching, but never quite reaching, the full value of E. However, at the end of 5 time constants (5RC), vC has reached 99.3% of E. This is considered close enough for practical purposes, and the capacitor is deemed fully charged at the end of this period of time.

baijin232911

老外总是把复杂的东西简单化，值得我们去学习的

lukeluck

0 _( ?/ D% @% V8 k  {" \% J
同理 电感电阻组成的LR电路也存在LR时间常数

czxjuren

学习了

wistful555

Mark一下。。。

AD9_PCB

yeah,it is right

zltwin

学习了

北漂的木木

我不认识它，它也不认识我。。。。

WuJin_eOakJ

学习了

zb213015

就是普通物理的量纲的转换

Soarphys

专业名词叫量纲分析，so easy！物理专业出身的应该都会

lukeluck

Soarphys 发表于 2018-4-27 08:30
专业名词叫量纲分析，so easy！物理专业出身的应该都会

8 `. M) S2 k: p; S! K0 I学电的也很少在教科书里看到 可能是中国学生的教科书内容有漏吧。

clp783

不知道说什么，感觉好厉害的样子。

Soarphys

lukeluck 发表于 2018-5-3 11:03
学电的也很少在教科书里看到 可能是中国学生的教科书内容有漏吧。

除了量纲分析，还有一个基本技能就是数量级估算，可以说量纲分析和数量级估算是物理学定性分析和半定量计算的两大法宝。数量级估算用到电路中有个比较典型的例子就是，电子运动速度的估算1/2mv2=2/3 KT;
( P# j4 N2 W. Q7 B0 V

lukeluck

Soarphys 发表于 2018-5-21 18:59
- G' {- y4 ]' y) q除了量纲分析，还有一个基本技能就是数量级估算，可以说量纲分析和数量级估算是物理学定性分析和半定量计 ...

这个截图是某个公开课程吧？有没有链接呢？