The Effective Value of an Alternating Current or

The Effective Value of an Alternating Current (or Voltage) © David Hoult 2009

If the two bulbs light to the same brightness (that is, they have the same power) then it is reasonable to consider the current Iac to be (in some ways) equivalent to the current Idc

If the two bulbs light to the same brightness (that is, they have the same power) then it is reasonable to consider the current Iac to be (in some ways) equivalent to the current Idc The simple average value of a (symmetrical) a. c. is equal to

If the two bulbs light to the same brightness (that is, they have the same power) then it is reasonable to consider the current Iac to be (in some ways) equivalent to the current Idc The simple average value of a (symmetrical) a. c. is equal to zero

The R. M. S. Value of an Alternating Current (or Voltage)

If an a. c. supply is connected to a component of resistance R, the instantaneous power dissipated is given by

If an a. c. supply is connected to a component of resistance R, the instantaneous power dissipated is given by power = i 2 R

The mean (average) power is given by

The mean (average) power is given by mean power = (mean value of i 2) R

The mean value of i 2 is

The mean value of i 2 I 2 is 2

The square root of this figure indicates the effective value of the alternating current

The square root of this figure indicates the effective value of the alternating current r. m. s. = root mean square

Irms = I 2 where I is the maximum (or peak) value of the a. c.

The r. m. s. value of an a. c. supply is equal to the direct current which would dissipate energy at the same rate in a given resistor

The r. m. s. value of an a. c. supply is equal to the direct current which would dissipate energy at the same rate in a given resistor We can use the same logic to define the r. m. s. value of the voltage of an alternating voltage supply.

The r. m. s. value of an a. c. supply is equal to the direct current which would dissipate energy at the same rate in a given resistor We can use the same logic to define the r. m. s. value of the voltage of an alternating voltage supply. Vrms = V 2 where V is the maximum (or peak) value of the voltage

We have been considering a sinusoidal variation of current (or voltage)

We have been considering a sinusoidal variation of current (or voltage)

We have been considering a sinusoidal variation of current (or voltage) For this variation, the r. m. s. value would be

We have been considering a sinusoidal variation of current (or voltage) For this variation, the r. m. s. value would be equal to the maximum value