Electrical Engineering Asked on January 4, 2022
While searching for something totally unrelated to this, I came a cross a website that derived it in this fashion:
the instanteous power in a capacitor is given by $$p_c= v_c(t)cdot i_c$$
since $$i_c(t) = Cfrac{dv_c}{dt}$$, this becomes $$p_c = v_c(t)cdot Cfrac{dv_c}{dt}$$
No issues so far….but, he then proceeds to write:
$$frac{dw_c(t)}{dt}=frac{d}{dt}[frac{1}{2}Cv_c^2(t)]$$.
power is the derivative of energy, so I get the left hand side of the equation. However, how does $$Cfrac{dv_c}{dt}cdot v_c(t)=frac{d}{dt}[frac{1}{2}Cv_c^2(t)]$$ on the right hand side of the equation?
Just use the chain rule of calculus:
$frac{d}{dt}v_c^2(t) = 2v_c(t)frac{dv_c(t)}{dt}$
therefore $v_c(t)frac{dv_c(t)}{dt} = frac{1}{2}frac{d[v_c^2(t)]}{dt}$
Answered by rpm2718 on January 4, 2022
3 Asked on December 13, 2020
0 Asked on December 13, 2020 by freddie
1 Asked on December 13, 2020 by ridham
3 Asked on December 12, 2020 by marcelo-queirs
2 Asked on December 12, 2020 by rijik
1 Asked on December 11, 2020 by tschaboo
2 Asked on December 11, 2020 by tarti
2 Asked on December 10, 2020 by mostafanfs
2 Asked on December 10, 2020 by easyohm
2 Asked on December 10, 2020
1 Asked on December 9, 2020 by steelixb
1 Asked on December 8, 2020 by user158568
2 Asked on December 8, 2020 by jrvinayak
1 Asked on December 7, 2020 by sim-son
0 Asked on December 7, 2020 by mmm
1 Asked on December 7, 2020 by cpuguru
1 Asked on December 5, 2020 by aditya-prajapati
constant current heatsink high current high voltage power supply
3 Asked on December 5, 2020 by smake5730
Get help from others!
Recent Questions
Recent Answers
© 2023 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP, SolveDir