RC time constant

The RC time constant, denoted τ (lowercase <a href="/facts/Tau/gfvnmJoH">tau</a>), the <a href="/facts/Time_constant/5na4AbzV">time constant</a> of a <a href="/facts/Resistor%E2%80%93capacitor_circuit/6WCu8sAc">resistor–capacitor circuit</a> (RC circuit), is equal to the product of the circuit <a href="/facts/Electrical_resistance_and_conductance/hxSt0UAj">resistance</a> and the circuit <a href="/facts/Capacitance/0pH046TL">capacitance</a>:

τ
        =
        R
        C
        
        .
      
    
    {\displaystyle \tau =RC\,.}

It is the <a href="/facts/Time/HceJKUGB">time</a> required to charge the <a href="/facts/Capacitor/hyowqv7n">capacitor</a>, through the <a href="/facts/Resistor/JrsGReM6">resistor</a>, from an initial charge voltage of zero to approximately 63.2% of the value of an applied <a href="/facts/Direct_current/r9MNUx84">DC voltage</a>, or to discharge the capacitor through the same resistor to approximately 36.8% of its initial charge voltage. These values are derived from the mathematical constant <a href="/facts/E_(mathematical_constant)/coEtSBk8">e</a>, where 
 
 
 
 63.2
 %
 ≈
 1
 
 −
 
 
 e
 
 −
 1
 
 
 
 
 {\displaystyle 63.2\%\approx 1{-}e^{-1}}
 
 and 
 
 
 
 36.8
 %
 ≈
 
 e
 
 −
 1
 
 
 
 
 {\displaystyle 36.8\%\approx e^{-1}}
 
. When using the <a href="/facts/International_System_of_Units/S7YLglNz">International System of Units</a>, R is in <a href="/facts/Ohm/QNVrlGjw">ohms</a>, C is in <a href="/facts/Farad/gPAYcVoE">farads</a>, and τ is in <a href="/facts/Second/jtFxnJXx">seconds</a>.
Discharging a capacitor through a <a href="/facts/In_series/007qC7j8">series</a> resistor to zero volts from an initial voltage of V0 results in the capacitor having the following <a href="/facts/Exponential_decay/wLB1zYDP">exponentially-decaying</a> voltage curve:

V
          
            C
          
        
        (
        t
        )
        =
        
          V
          
            0
          
        
        ⋅
        (
        
          e
          
            −
            t
            
              /
            
            τ
          
        
        )
      
    
    {\displaystyle V_{\text{C}}(t)=V_{0}\cdot (e^{-t/\tau })}

Charging an uncharged capacitor through a series resistor to an applied constant input voltage V0 results in the capacitor having the following voltage curve over time:

V
          
            C
          
        
        (
        t
        )
        =
        
          V
          
            0
          
        
        ⋅
        (
        1
        −
        
          e
          
            −
            t
            
              /
            
            τ
          
        
        )
      
    
    {\displaystyle V_{\text{C}}(t)=V_{0}\cdot (1-e^{-t/\tau })}

which is a vertical <a href="/facts/Mirror_image/xkbUhBzI">mirror image</a> of the charging curve.

RC time constant open-in-new

RC time constant