Capacitors connected in series with resistors can introduce delay which is extremely important in electronics. It works on the very simple principle, shown in the figure below.
(Source: referenced)
When the switch is closed, the current flows and the capacitor starts to charge, trying to reach the voltage of the source to which it is exposed. The capacitor is charged through a resistor that resists the flow of current, so it will take some time until the capacitor is fully charged. This time is marked as the time constant and is calculated by multiplying the resistance of the resistor and the capacitance of the capacitor according to the formula:
Judging by the graph, it takes 5-time constants (5T) to fully charge the capacitor. To arrive at the half voltage value, the capacitor is charged at 0.7T. For example in the figure, it is easy to calculate the time constant:
The voltage on the capacitor will need 5T or 5 seconds to reach a value of 5V. In order to reach the value of 2.5V, the capacitor will need 0.7T or 0.7 seconds. Let us try to prove that with an experiment.
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