RL Circuit - Important Formulas

Circuit: A series R and inductor L connected to a DC source V at t = 0

• Current
  • $i_L(t)=I_{\infty }[1-e^{-\frac{t}{\tau }}]$
  • $I_{\infty }=\frac{V}{R}$
  • $\tau =\frac{L}{R}$
• Voltage Across Inductor
  • $v_L(t)=L\frac{d{i}_L}{dt}=V{e}^{-\frac{t}{\tau }}$
• RL Discharge (initial inductor current $I_0$)
  • $i_L(t)=I_0{e}^{-\frac{R}{L}t}$