RC Charging Circuit

All Electrical and Electronic circuits or systems suffer from some kind of "time delay" between the input and output terminals, when a continuous (DC) or alternative (AC) signal or voltage is applied to it.

This delay is usually known as circuit time delay or Time Constant, which represents the time response of the circuit when an input step voltage or signal is applied. The resulting time constant of any electronic circuit or system will depend mainly on the capacitive or inductive reactive components attached to it. Has time constant units, Tau – τ

When an increased DC voltage is applied to an emptied Capacitor, the capacitor pulls what is called "charging current" and "charging". When this voltage decreases, the capacitor begins to discharge in the opposite direction. Because capacitors can store electrical energy, they move in many ways, such as small batteries. They store or release energy as needed on their plates.

The electrical charge stored on the plates of the capacitor is given as follows: Q = CV. Charging (storing) and discharging (releasing) a capacitor energy in this way is never instantaneous, but it takes a certain amount of time for the capacitor to be charged or discharged up to a certain percentage of the maximum feed value known as the time constant (τ).

If a resistance is serially connected with the capacitor that creates an RC circuit, the capacitor gradually charges along the resistance until the voltage reaches the supply voltage. The time required to fully charge the capacitor is equivalent to approximately 5 time constants or 5T. therefore, a temporary response or a series of RC circuits is equivalent to 5 time constants.

This transient response time is measured in t, τ = R X C seconds. Where r is the value of resistance in ohm. C is the value of the capacitor in the farces. This then forms the basis of an RC charging circuit and the 5T can be considered.

RC Charging Circuit

Above, let's say that the C capacitor is completely "discharged" and the (S) switch is completely open. These are the initial conditions of the circuit, then t = 0, i = 0 and q = 0. When the switch is turned off, the time starts at t = 0 and the current begins to flow through the resistance to the capacitor.

RC Charging Circuit
RC Charging Circuit

Above, let's say that the capacitor, C is completely "discharged" and the switch (s) is completely on. These are the initial conditions of the circuit. Then t = 0, I = 0, and q = 0. When the switch is turned off, the time starts at t = 0 and the current begins to flow through the resistance to the capacitor.

Since the initial voltage on the capacitor is zero, at ( Vc = 0 ) t = 0, the capacitor looks like a short circuit to the outer circuit, and the maximum current passes through the circuit, which is limited only by resistance R. Then, using Kirchhoff, the voltage law (KVL), voltage drops around the circuit are given as follows:

RC Charging Circuit

The current flowing around the circuit is called the charging current and is found using the Ohm Act: i = Vs / R.

RC Charging Circuit Curves

RC Charging Circuit
RC Charging Circuit Curves

The capacitor (C) charges at a rate indicated by the graph. The increase in the RC charging curve is much steeper at the beginning, since the charging speed is the fastest at the beginning of charging, but it shrinks exponentially as the capacitor receives additional charging at a slower speed.

When the capacitor is charging, the potential difference between its plates begins to increase with the actual time it takes for the load on the capacitor to reach 63% of the maximum possible full-charge voltage, 0.63 Vs, known as a full-time constant in our curve, (T).

This 0.63 Vs voltage point is given an abbreviation of 1T (a time constant).

The capacitor continues to charge and the voltage and circuit current difference between Vs and Vc is also decreasing. So then in its last case, when it is said that the capacitor is fully charged, it is larger than the five time constants ( 5T ), t = ∞, i = 0, q = Q = CV. Horse

In infinity, the charging current finally drops to zero and acts as an open circuit with a completely feed voltage value throughout the capacitor as Vc = Vs. Therefore, mathematically, we can say that the time (1T) required for charging a capacitor up to a time constant is given as follows:

RC Time Constant, Tau

RC Charging Circuit

This RC time constant only indicates a charging rate at which R is Ω and Farads have C.

Since voltage V, equation, relates to the load on a capacitor given with VC = Q/C, the voltage along the capacitor (Vc) at any time during the charging period is given as follows:

RC Charging Circuit

After a period equivalent to 4 time constants, (4T) it is said that the capacitor in this RC charging circuit is almost fully charged, since the voltage developed along the capacitor plates has reached 98% of its maximum value, 0.98 Vs. the time it takes for the capacitor to reach this 4T point is known as the temporary time.

After a period of 5T, it is said that the capacitor is fully charged with a voltage equal to the supply voltage (Etc. along the capacitor ( Vc). Therefore, since the capacitor is fully charged, no more charging currents flow in the circuit. Therefore, IC = 0. The time period after this 5T time period is often known as a stable state period.

Then in the table below we can show the percentage voltage and current values for the capacitor in an RC charging circuit for a specific time constant.

RC Charging Table

RC Charging Circuit

Note that the charging curve for an RC charging circuit is not exponential and linear. This means that in reality the capacitor is never fully charged 100%. Therefore, it reaches a load of 99.3% after five time constants (5T) for all practical purposes. Therefore, at this point the capacitor is considered to be fully charged.