where at t = 0, Q0 = CE. , then the magnitude of the current as a function of time is given by: I = Since = IR, then as a function of time is ∆VR ∆VR = ∆VR Since = Q/C, then as a function of time is ∆VC ∆VC = ∆VC (V-23 #3) In the same way that we did for the charging circuit, find the following: I (at t = 0) = ____________ Q (at t = 0) = ____________ (at t = 0) = ____________ (at t = 0) = ____________ ∆VR ∆VC (V-24 #1) After a long time (t ~ ∞) I (at t = 0) = ____________ Q (at t = 0) = ____________ (at t = 0) = ____________ (at t = 0) = ____________ ∆VR ∆VC (V-24 #2) Again these should correspond to the limiting values of these quantities on your graphs at the bottom of page V-20.  The RC Time Constant (Greek letter tau) A useful parameter for describing RC circuits is the time required for the exponential term to become e-1. This occurs when t = RC. This time is defined as the RC time “”  constant, = RC. It is a measure of the speed with which the current and voltage change  in an RC circuit. For example, in discharging a capacitor, in one time constant (when t = = RC) the charge becomes Q = Q0(e-1) = Q0/e 0.37Q0 , In words, in one Q has decreased to ~37% of it’s original value. Similarly, in charging a capacitor, in 1 the charge becomes Q = Q0(1 e-1) 0.63Q0 – or 63% of its maximum value.
where at t = 0, Q0 = CE. , then the magnitude of the current as a function of time is given by: I = Since ∆VR = IR, then ∆VR as a function of time is ∆VR = Since ∆VC = Q/C, then ∆VC as a function of time is ∆VC = (V-23 #3) In the same way that we did for the charging circuit, find the following: I (at t = 0) = ____________ Q (at t = 0) = ____________ ∆VR (at t = 0) = ____________ ∆VC (at t = 0) = ____________ (V-24 #1) After a long time (t ~ ∞) I (at t = 0) = ____________ Q (at t = 0) = ____________ ∆VR (at t = 0) = ____________ ∆VC (at t = 0) = ____________ (V-24 #2) Again these should correspond to the limiting values of these quantities on your graphs at the bottom of page V-20. The RC Time Constant  (Greek letter tau) A useful parameter for describing RC circuits is the time required for the exponential term to become e-1. This occurs when t = RC. This time is defined as “” the RC time constant,  = RC. It is a measure of the speed with which the current and voltage change in an RC circuit. For example, in discharging a capacitor, in one time constant (when t =  = RC) the charge becomes Q = Q0(e-1) = Q0/e 0.37Q0 In words, in one , Q has decreased to ~37% of it’s original value. Similarly, in charging a capacitor, in 1 the charge becomes Q = Q0(1 – e-1) 0.63Q0 or 63% of its maximum value.
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