#### Loki

Can anyone help me with this homework problem? I worked it through, but the answer i get doesn't agree with the answer the book gives. I'll include my work, and if anyone can help, I'll be eternally grateful, at least for a while.

The Problem:

My Work:

[tex]P_r = 2 P_{nr}[/tex]

[tex]P = I * V * \cos \phi[/tex]

[tex]\phi = \arctan \frac{X_L - X_C}{R} [/tex]

At resonant frequency, [itex]X_L - X_C = 0[/itex]

[tex]I * V * \cos ( \arctan \frac{X_L-X_C}{R} ) = 2 * I * V \cos (\arctan\frac{X_L-X_C}{R})[/tex]

[tex]I * V * \cos ( \arctan (0)) = 2 * I * V \cos (\arctan\frac{X_L-X_C}{R})[/tex]

[tex]I * V * \cos (0) = 2 * I * V \cos (\phi)[/tex]

[tex] 1 = 2 \cos (\phi)[/tex]

[tex]\cos \phi = \frac{1}{2}[/tex]

This seems correct to me, but the book says the answer is [itex]\frac{\sqrt {2}}{2}[/itex]

Am I mistaking the "Factor of two" part of the problem? Does this really mean that the power is squared?

If anybody can help, thanks. On a sidenote, LaTeX is very nice, if a bit tedious to write in.

The Problem:

In a series RCL circuit the dissapated power drops by a factor of two when the frequency of the generator is changed from the resonant frequency to a nonresonant frequency. The peak voltage is held constant while this change is made. Determine the power factor of the curcuit at nonresonant frequency.

My Work:

[tex]P_r = 2 P_{nr}[/tex]

[tex]P = I * V * \cos \phi[/tex]

[tex]\phi = \arctan \frac{X_L - X_C}{R} [/tex]

At resonant frequency, [itex]X_L - X_C = 0[/itex]

[tex]I * V * \cos ( \arctan \frac{X_L-X_C}{R} ) = 2 * I * V \cos (\arctan\frac{X_L-X_C}{R})[/tex]

[tex]I * V * \cos ( \arctan (0)) = 2 * I * V \cos (\arctan\frac{X_L-X_C}{R})[/tex]

[tex]I * V * \cos (0) = 2 * I * V \cos (\phi)[/tex]

[tex] 1 = 2 \cos (\phi)[/tex]

[tex]\cos \phi = \frac{1}{2}[/tex]

This seems correct to me, but the book says the answer is [itex]\frac{\sqrt {2}}{2}[/itex]

Am I mistaking the "Factor of two" part of the problem? Does this really mean that the power is squared?

If anybody can help, thanks. On a sidenote, LaTeX is very nice, if a bit tedious to write in.

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