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

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Presentation on theme: "The Effective Value of an Alternating Current (or Voltage) © David Hoult 2009."— Presentation transcript:

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

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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 I ac to be (in some ways) equivalent to the current I dc © David Hoult 2009

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 I ac to be (in some ways) equivalent to the current I dc The simple average value of a (symmetrical) a.c. is equal to © David Hoult 2009

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 I ac to be (in some ways) equivalent to the current I dc The simple average value of a (symmetrical) a.c. is equal to zero © David Hoult 2009

10 The R.M.S. Value of an Alternating Current (or Voltage) © David Hoult 2009

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12 If an a.c. supply is connected to a component of resistance R, the instantaneous power dissipated is given by © David Hoult 2009

13 If an a.c. supply is connected to a component of resistance R, the instantaneous power dissipated is given by power = i 2 R © David Hoult 2009

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16 The mean (average) power is given by © David Hoult 2009

17 The mean (average) power is given by mean power = (mean value of i 2 ) R © David Hoult 2009

18 The mean value of i 2 is © David Hoult 2009

19 The mean value of i 2 is I2I2 2 © David Hoult 2009

20 The square root of this figure indicates the effective value of the alternating current © David Hoult 2009

21 r.m.s. = root mean square The square root of this figure indicates the effective value of the alternating current © David Hoult 2009

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23 I rms = where I is the maximum (or peak) value of the a.c. I 22 © David Hoult 2009

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 © David Hoult 2009

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. © David Hoult 2009

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 rms = V 22 where V is the maximum (or peak) value of the voltage © David Hoult 2009

27 We have been considering a sinusoidal variation of current (or voltage) © David Hoult 2009

28 We have been considering a sinusoidal variation of current (or voltage) © David Hoult 2009

29 We have been considering a sinusoidal variation of current (or voltage) For this variation, the r.m.s. value would be © David Hoult 2009

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 © David Hoult 2009


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