RC Circuit - Important Formulas

Circuit: A series resistor R and capacitor C connected to a DC source V at t = 0

• Voltage Across Capacitor:
  • $v_C(t)=V_{\infty }[1-e^{-\frac{t}{r}}]$
  • $V_{\infty }=V$
  • $\tau =RC$
• Current Through Capacitor
  • $i_C(t)=\frac{v_C(t)}{R}=\frac{V}{R}{e}^{-\frac{t}{r}}$
• RC Discharge
  • $v_C(t)=V_0{e}^{-\frac{t}{RC}}$
  • $i_C(t)=\frac{v_C(t)}{R}$