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

Electric Circuits [EXP-19836]

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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