text: # 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
  7,316
  1,571
  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.)