0
\$\begingroup\$

We know that voltage across a capacitor is given by

enter image description here

But there is this other formula

enter image description here

How this second formula was deducted mathematically from the first one? or from another one?

\$\endgroup\$
3
  • \$\begingroup\$ in the second formula, what is R, \$V_s\$ and \$V_c\$? You need to explain it to us \$\endgroup\$ – FrancoVS Jun 26 '18 at 11:18
  • \$\begingroup\$ @FrancoVS - Vc should be voltage on capacitor. Vs will be the source voltage. \$\endgroup\$ – Whiskeyjack Jun 26 '18 at 11:29
  • \$\begingroup\$ Do you know how to solve an ODE? \$\endgroup\$ – Spehro Pefhany Jun 26 '18 at 11:31
1
\$\begingroup\$

Let I_r be current in the resistor = Vc/R at any time.

  • Vc = Q/C from the basic definition of capacitance.

  • dQ/dt = -I_r = -Vc/R From the basic definition of current.

  • dQ/dt = -Q/CR

Apply initial conditions, Q at time 0 = Vs * C and do trivial calculus, then substitution to get Vc in place of Q.

\$\endgroup\$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.