# Time Constant Formula

All electronic circuits experience some kind of “time-delay” between its output and input when a voltage, either DC or AC is applied to it. This delay is termed as the Time Constant or the time delay of an electric circuit. The resultant time constant of an electric circuit depends on reactive components either inductive or capacitive connected to it. The capacitor charges up when a DC voltage (increasing) is applied to it while it is discharged. The capacitor discharges (opposite direction) when the voltage is decreased. Due to these properties of a capacitor, they act like small batteries and are capable of releasing or storing the energy as required. The charge of the capacitor plate is given as Q = VC. This charging and discharging of capacitors doesn’t happen instantly but take a certain amount of time. The time required in charging or discharging the capacitor to a specific percentage of its highest supply value is called as its Time Constant, denoted by Tau (τ).

## Universal Time Constant Formula

$Change=(Final - Start)(1-\frac{1}{e^{t/\tau }})$
Where,
Final = Value of calculated variable after infinite time
Start = Initial value of the calculated variable
e = Euler’snumber (2.7182818)
t =Time in seconds
τ =Time constant for the circuit in seconds

### Follow the following steps to analyse an RC and L/R circuit

Step 1: Determine the time constant of the circuit
Step 2: Identify the quantity to be calculated (the quantity whose change is opposed by the reactive component)
Step 3: Find the starting and final values of that quantity.
Step 4: Substitute all the values determined in the Universal Time Constant formula and then find Change in quantity.
Step 5: If the starting value is zero then the change in quantity is equal to the value calculated using the formula. If not, add the change to the starting value to find the answer.
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