# capacitors

Discussion in 'General Electronics Chat' started by kaz21, Jul 10, 2011.

1. ### kaz21 Thread Starter New Member

Jun 11, 2011
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How to derive a mathematical relationship for the voltage across a capacitor in the transient stage of charging the capacitor??The voltage source is a dc voltage source.

2. ### ErnieM AAC Fanatic!

Apr 24, 2011
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A device that holds a charge Q and has voltage V across has a capacitance of:

$C = \fra{Q(t)}{V(t)}$

Solving for Q(t):

$Q(t) = C V(t)$

Noting that the total charge is the integral of current, or

$\int I(t) dt = Q(t)$

We can substitute for Q(t):

$Q(t) = \int I(t) dt = C V(t)$

If we differentiate by t we get the traditional relationship between voltage and current:

$I(t) = C \fra {dV(t)} {dt}$

Solving for $dV(t)$:

$dV(t) = \fra {1} {C} I(t) dt$

Integrate both sides:

$V(t) = \fra{1}{C}\int I(t) dt$ (limits of -∞ to t)

(I somehow suspect this is not the answer you were looking for.)