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Explanation & Answer
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Experiment No. 4:
The RC Time Constant
Name
Morgan State University Department of Physics
October 3, 2017
Introduction
Resistor-Capacitor (RC) circuit is a circuit that contains both a capacitor (C) and a resistor
(R) in series with a voltage source of emf (ε) (1). Aside from being a common element in electronic
device, RC circuits also play an important role in the electrical signal transmission in brain cells
(2).
Consider the simple RC circuit diagram in Figure 1 below.
Figure 1. Simple RC circuit
Once the circuit is closed, the charge and voltage of the capacitor, which is initially zero, increases
exponentially with time until the charge, Q, is equal to Cε and voltage, VC, becomes equal to ε.
The charging of the capacitor can then be described by equation 1:
𝑡
𝑄 = 𝐶𝜀 (1 − 𝑒 −𝑅𝐶 )
(Equation 1)
The parameter RC can be referred to as the time constant of the circuit and is expressed in terms
of seconds. This time constant RC is used to indicate how fast a capacitor can reach approximately
two-thirds of its capacity. When the time is much greater than RC, the capacitor is fully charged
and its Q is equal to Cε and its VC is equal to ε.
Once the voltage source of a circuit with a fully-charged capacitor was removed, the capacitor
immediately begins to discharge through the resistor, the discharging process of the capacitor can
then be described as follows:
𝑡
𝑄 = 𝐶𝜀𝑒 −𝑅𝐶
(Equation 2)
When the time is equal to the time constant RC, approximately only a third of the original charge
of the capacitor remains. Once the time is comparatively ...