RC Time Constant Calculator

The RC time constant, represented as τ (tau), is a measure used in electrical engineering to quantify the time it takes for a capacitor, through a resistor, to charge to approximately 63.2% of the voltage supply or discharge to about 36.8% of its initial charge voltage.

Calculator

Enter

  • Resistance R with units ohm (Ω)
  • Capacitance C with units Farad (F)

	

			

		

						

				

				

                

			

			
						

		

		






Formula





τ = R*C





Where 





    

  • R is the resistance in ohm (Ω)
    • 




  • C is the capacitance in Farad (F)
    • 




  • τ is the time constant in seconds
    • 






Example Calculation





For a resistor value of 1 ohm and Capacitor value of 10 µF, the time constant is 10 µs.





Application





The significance of the RC time constant lies in its utility for predicting how quickly a circuit responds to a change in voltage. 





For instance, in a charging capacitor scenario, the voltage across the capacitor at any time ( t ) can be calculated using the formula:





Vc = Vi (1-e-t/τ)





where,





    

  • Vi = Input Voltage
    • 




  • τ = time constant
    • 




  • Vc = voltage at the capacitor at time t
    • 






time constant τ = RC, where R is resistance and C is capacitance.





Similarly, for a discharging capacitor, the voltage across it decreases over time following the exponential decay formula:





V = Vo*e−t/RC





The time constant time constant τ = RC, where R is resistance and C is capacitance. The time t is typically specified as a multiple of the time constant.





t = RC*Loge(Vo/V)





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