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Question 10.3: a) A sinusoidal voltage having a maximum amplitude of 625 V ...

a) A sinusoidal voltage having a maximum amplitude of 625 V is applied to the terminals of a 50 Ω resistor. Find the average power delivered to the resistor.
b) Repeat (a) by first finding the current in the resistor.

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a) The rms value of the sinusoidal voltage is \frac{625}{\sqrt{12}} , or approximately 441.94 V. From Eq. 10.19 P =\frac{V^{2}_{rms}}{R} , the average power delivered to the 50 Ω resistor is

P =\frac{\left(441.94\right)^{2}}{50} = 3906.25 W.

b) The maximum amplitude of the current in the resistor is 625/50, or 12.5 A. The rms value of the current is \frac{12.5}{\sqrt{2}} , or approximately 8.84 A. Hence the average power delivered to the resistor is

P =\left(8.84\right)^{2}50 = 3906.25 W.

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