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Capacitor Charging Graph

Capacitor Charging Graph

 A voltage-time graph for a charging capacitor. The target voltage and time constant are labelled.

The charging current asymptotically approaches zero as the capacitor becomes charged up to the battery voltage. Charging the capacitor stores energy in the electric field between the capacitor plates. The rate of charging is typically described in terms of a time constant RC.

In physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI (linear time-invariant) system.

The RC Time Constant:

All Electrical or Electronic circuits or systems suffer from some form of “time-delay” between its input and output, when a signal or voltage, either continuous, ( DC ) or alternating ( AC ) is firstly applied to it. This delay is generally known as the time delay or Time Constant of the circuit and it is the time response of the circuit when a step voltage or signal is firstly applied.

The resultant time constant of any Electronic Circuit or system will mainly depend upon the reactive components either capacitive or inductive connected to it and is a measurement of the response time with units of, Tau – τ

When an increasing DC voltage is applied to a discharged Capacitor, the capacitor draws a charging current and “charges up”, and when the voltage is reduced, the capacitor discharges in the opposite direction. Because capacitors are able to store electrical energy they act like small batteries and can store or release the energy as required.

The charge on the plates of the capacitor is given as: Q = CV. This charging (storage) and discharging (release) of a capacitors energy is never instant but takes a certain amount of time to occur with the time taken for the capacitor to charge or discharge to within a certain percentage of its maximum supply value being known as its Time Constantτ ).

If a resistor is connected in series with the capacitor forming an RC circuit, the capacitor will charge up gradually through the resistor until the voltage across the capacitor reaches that of the supply voltage. The time also called the transient response, required for the capacitor to fully charge is equivalent to about 5 time constants or 5T.

This transient response time T, is measured in terms of τ = R x C, in seconds, where R is the value of the resistor in ohms and C is the value of the capacitor in Farads. This then forms the basis of an RC charging circuit were 5T can also be thought of as “5 x RC”.

 

RC Charging Table:

Time ConstantRC ValuePercentage of Maximum
VoltageCurrent
0.5 time constant0.5T = 0.5RC39.3%60.7%
0.7 time constant0.7T = 0.7RC50.3%49.7%
1.0 time constant1T = 1RC63.2%36.8%
2.0 time constants2T = 2RC86.5%13.5%
3.0 time constants3T = 3RC95.0%5.0%
4.0 time constants4T = 4RC98.2%1.8%
5.0 time constants5T = 5RC99.3%0.7%
 

Note that as the charging curve for a RC charging circuit is exponential, the capacitor in reality never becomes 100% fully charged due to the energy stored in the capacitor. So for all practical purposes, after five time constants a capacitor is considered to be fully charged.

 

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