The Effective Value of an Alternating
Current (or Voltage)
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
© 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
© 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
The simple average value of a (symmetrical) a.c. is
equal to
© 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
The simple average value of a (symmetrical) a.c. is
equal to zero
© David Hoult 2009
The R.M.S. Value of an Alternating Current (or
Voltage)
© David Hoult 2009
© David Hoult 2009
If an a.c. supply is connected to a component of
resistance R, the instantaneous power dissipated
is given by
© David Hoult 2009
If an a.c. supply is connected to a component of
resistance R, the instantaneous power dissipated
is given by power = i2 R
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
The mean (average) power is given by
© David Hoult 2009
The mean (average) power is given by
mean power = (mean value of i2) R
© David Hoult 2009
The mean value of i2 is
© David Hoult 2009
The mean value of
i2
I2
is
2
© David Hoult 2009
The square root of this figure indicates the
effective value of the alternating current
© David Hoult 2009
The square root of this figure indicates the
effective value of the alternating current
r.m.s. = root mean square
© David Hoult 2009
© David Hoult 2009
Irms =
I
2
where I is the maximum (or peak) value of the a.c.
© David Hoult 2009
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
© David Hoult 2009
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.
© David Hoult 2009
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
© David Hoult 2009
We have been considering a sinusoidal variation
of current (or voltage)
© David Hoult 2009
We have been considering a sinusoidal variation
of current (or voltage)
© David Hoult 2009
We have been considering a sinusoidal variation
of current (or voltage)
For this variation, the r.m.s. value would be
© David Hoult 2009
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
© David Hoult 2009