The form factor and peak factor The Average Value The Effective rms Value To explain this equation let Then Since the average value of the second term equal to zero then the only constant term ID: 1031330
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1. Lecture 4-2The maximum, average and effective value.The form factor and peak factor.
2. The Average Value
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11. The Effective (rms) Value
12. To explain this equation let:ThenSince the average value of the second term equal to zero, then the only constant term will represent the dissipated power during the heating process time.
13. Note:Three processes are done on the AC current in the above derivation to find its effective value, these are:The AC current is squared.The average value of the squared current is adopted.The effective current determined by finding the square root of the mean of the squared current. Hence, the effective value of the AC sinusoidal current is “the root of the mean of its square value, so it is known as the rms value”.
14. Example:Let us consider the behavior of an Ironing Machine ( المكواة) as a pure resistive load of 1kW power supplied by a single phase AC voltage of (220V, 50Hz) for domestic application.The supplied voltage can be represented mathematically as:Since its rms value is 220V, then its maximum value () is:Then Since,Then The time domain function of the current is already known as:
15. Example:Let us consider the behavior of an Ironing Machine ( المكواة) as a pure resistive load of 1kW power supplied by a single phase AC voltage of (220V, 50Hz) for domestic application.The supplied voltage can be represented mathematically as:Since its rms value is 220V, then its maximum value () is:Then Since,Then The time domain function of the current is already known as:
16. Then In time domain and due to Kirchhoff's Voltage Law (KVL) in a closed circuitAlso,OrThen And from the previous derivation, the time domain function of the power is:Now, the time domain functions or the instantaneous values of:the source and load voltages the supplied current the consumed powerAre determined and can be represented as follows:
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18. The Form Factor and Peak FactorSince, the effective value or the (rms) value is And the average value is:Then the Form Factor is:Also, the Peak Factor or Crest Factor=Hence, for any sinusoidal function like AC current or Voltage
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