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Module 1: Capacitors

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The time constant

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XSIQ
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Physics - The time constant

The time constant

Trying to determine the amount of time that it takes to fully charge a
capacitor is difficult. The exponential nature of the voltage accumulation
process means that the capacitor approaches its maximum voltage value
gradually. As the graph below shows, it is nearly fully charged for a
considerable part of the process. For convenience, a term called the time
constant [1] was defined. A period of one time constant is the time it
takes to charge the capacitor by 63% or approximately two-thirds of its
maximum value. It takes five full time constants for the capacitor to
become fully charged.

Time constants are not specified for capacitors as the constants affected
by the other components in the circuit. Obviously if less current is able
to flow in a circuit then the capacitor will take longer to become fully
charged. Also, the larger the capacitance of the capacitor the longer it
will take to charge.

The time constant is therefore determined by both the capacitance of the
capacitor and the total resistance of the circuit.

Calculate the time constant for the circuit shown below. How long would it
take to fully charge the capacitor?

Since it takes five time constants to fully charge a capacitor, it would
take (0.3 x 5) or 1.5 seconds to fully charge.

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