1.75 x 106F 7. When a resistor is connected by itself to an ac generato r, the a

Question

1.75 x 106F 7. When a resistor is connected by itself to an ac generato r, the average power delivered to it is Pave- Gen -1.000 W (I w). When a capacitor is added in series with the resistor, the power delivered is Pave- 05 w (without the capacitor), the power delivered is Pave-L-0.250 W. Find the power delivered when all the three elements, the capacitor, inductor and the resistor are connected, in series, to the same generator. When an inductor is added in series with the resistor only, R. VSín t

Explanation / Answer

P = Irms^2/ R = 1 W  

When capacitor is connected,

Now, I'rms^2 R = 0.5 W

so Irms / I'rms = sqrt(2) = 1.414

and Irms = V / Z  

Z = R and Z' = sqrt[R^2 + Xc^2]

so sqrtp R^2 + Xc^2] / R = 1.414

R^2 + Xc^2 = 2 R^2

so Xc = R

when inductor also connected,

Z" = sqrt[R^2 + XL^2]

so sqrt[R^2 + XL^2] / R = sqrt(1/0.250)

R^2 + XL^2 = 4 R^2

XL =1.732 R

when both connected,

Z = sqrt[R^2 + (XL - Xc)^2] = sqrt[R^2 + (0.732R)^2]

= 1.24 R

now P = 1 / 1.24 = 0.8 Watt ....Ans

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