How is Energy Exchanged in a Parallel Circuit?

AI Thread Summary
In a parallel circuit with a voltage source of 10√2 cos(2000t), a 10-ohm resistor, a 10mH inductor, and a 15μF capacitor, the energy exchanged between the source and the load is calculated to be 0.0962J, while the energy exchanged between the capacitor and inductor is 0.144J. There is a concern that the book's calculation of the equivalent impedance (Z_eq) may be incorrect, potentially leading to erroneous energy values. The correct Z_eq is found by adding the admittance of the components and inverting it, resulting in a value of 9.8 at an angle of 11.3 degrees. The energy calculations involve using the formulas for energy in inductors and capacitors, confirming that the load includes the resistor, inductor, and capacitor. The discussion emphasizes the importance of accurately determining Z_eq for correct energy exchange calculations.
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Homework Statement


All components arranged parallel,

voltage source =10sqrt(2)cos(2000t)
10 ohm resistor, 10mH inductor, 15 microF
How much energy is exchanged between the source and the load? (book answer: 0.0962J) Between the capacitor and the inductor? (0.144J)

But I think the book answer made a mistake in getting Z_eq which gave the wrong anwer. I think they left Z_eq invert and used it as Z_eq in calculation

Homework Equations


I_p = V_p / Z_eq
S =0.5 (V_P) (I_P*) -> giving a complex solution, where the real is P and I am is Q

Between source and load: W = Q/omega
Energy in inductor W = (0.5)( L )(I_P)^2
energy in capacitor W = (.5) (C) (V_p)^2

The Attempt at a Solution



Find the Z_eq by adding the admittance of the components, then invert it giving 9.8 with degree 11.3

Find I with the equation above 1.02 sqrt(2) degree -11.3

Find S giving Real(10) + Im(2) -> p=10 Q = 2

Energy between load and source: using omega = 2000 -> W = 2/1000 = 0.001

Energy between capacitor and inductor: I think it should be the energy of the inductor plus capacitor
 
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Is the load supposed to be the whole network, the resistor, or something else? Also, I think you are correct that it wants the energy of the inductor plus the capacitor.
 
Yes, The load consist of the resister, inductor and capacitor.
 

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