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

7. 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

8. 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

9. 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

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

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

13. If an a.c. supply is connected to a component of resistance R, the instantaneous power dissipated is given by power = i2 R

16. The mean (average) power is given by

17. The mean (average) power is given by
mean power = (mean value of i2) R

18. The mean value of i2 is

19. I2
The mean value of i2 is 2

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

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

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

24. 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

25. 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.

26. 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. V
Vrms = 2
where V is the maximum (or peak) value of the voltage

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

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

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

30. 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