When a resistor is connected by itself to an ac generator, the average power del

Question

When a resistor is connected by itself to an ac generator, the average power delivered to the resistor is 0.826 W. When a capacitor is added in series with the resistor, the power delivered is 0.397 W. When an inductor is added in series with the resistor (without the capacitor), the power delivered is 0.224 W. Determine the power dissipated when both the capacitor and the inductor are added in series with the resistor.Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

Explanation / Answer

Let:
v = generator voltage
i = current with C1 only
Xc1,Xc2 = reactance of C1,C2 respectively

Case 1.
v = i * Xc1

Case 2.
v = ( i/3) * (Xc1 + Xc2)

Substituting v, i disappears

Xc1 = (Xc1 + Xc2)/3

Xc2 = 2 * Xc1

Effective reactance of Xc1 and Xc2 in parallel

[1/Xp = (1/Xc1) + (1/Xc2)]

Xp = (Xc1 * Xc2)/(Xc1 + Xc2)
Substitute for Xc2 and simplify

Xp = 2 * Xc1 /3

The current will be v/(Xc1 * 2/3) = 1.5 * v/Xc1
= 1.5 * i
The current will increase by a factor of 1.5.

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