How to Calculate RC Constant

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The RC time constant is the time required to charge a capacitor to 63.2% of its full charge and discharge it to 36.8% of its initial voltage. In short, the RC constant is a measure of how quickly a capacitive circuit charges and discharges. The RC constant is calculated from the product of the circuit resistance and the circuit capacitance and is given in seconds. The RC time constant is denoted by the Greek sign, τ, and is derived from the following formula: T = R*C where R is circuit resistance and C is circuit capacitance.

  • Determine the resistance of the circuit. In a simple circuit with only one resistor and one capacitor, the total resistance of the circuit can be found by taking the resistance of the resistor. The value of the resistor determines the time it takes to charge or discharge the capacitor. Resistance in different circuit configurations is calculated as shown below:

    In Series:

    Rt = R1 + R2 .....Rn

    In Parallel:

    Rt = R1 R2 / R1 R2

    The total resistance is given in ohms.

  • Determine the circuit capacitance. Again, in a simple circuit with only one resistor and one capacitor, the capacitor capacitance is displayed on the capacitor and is given in micro-Farads. Capacitance in different circuit configurations is calculated as shown below:

    In Series:

    Ct = C1 C2 / C1 C2

    In Parallel:

    Ct = C1 + C2.....Cn

  • Compute the time constant of the circuit by finding the product of the resistance in ohms and the capacitance in Farads as shown below:

    T = R (in ohms) * C (in Farads)

Tips & Warnings

  • In a simple circuit, it is assumed that as time passes the capacitor charges and eventually attains the supply voltage. On the same note, the voltage across the resistor, during charging, eventually drops to zero. It can thus be deduced that the time constant is the time it takes for the capacitor voltage to attain the supply voltage and the time it takes for voltage across the resistor to fall to zero.
  • Laplace and Fourier transforms are used to derive functions and in analyzing linear time-invariant systems in electrical circuits.
  • Charging curves used in RC constant computations indicate that the charging rate is fastest at the start and slows down as time passes.
  • It takes about 5T (Time Constants) for the capacitor to be fully charged and for the capacitor voltage to equal the supply voltage.

References

  • Photo Credit Hemera Technologies/PhotoObjects.net/Getty Images
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