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knowlewj01
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Homework Statement
An electric motor draws a 1A (rms) from the 230V (rms) mains. and is found to shift the phase of the 50Hz alternating current by 30% of the period. What is the self inductance of the coils in the motor?
Homework Equations
The Attempt at a Solution
i've started by finding the phase shift:
[itex]\delta = \frac{3}{10}\cdot \frac{1}{f} = \frac{3}{10}\cdot\frac{1}{50} = 0.006[/itex]
i think the circuit has only an inductor and power source in it, so using kirchhoffs loop rule:
[itex] V_{max}cos(\omega t) - L\frac{dI}{dt} = 0[/itex]
seperate variables and integrate:
[itex]V_{max} \int cos(\omega t) dt = \int L dI[/itex]
[itex] \frac{V_{max}}{\omega}\cdot sin(\omega t) = LI[/itex]
sin(wt) = cos(wt - d)
[itex] L = \frac{V_{max}}{\omega I} cos(\omega t - \delta)[/itex]
I know everything here apart from t, is this the right way to do this?