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    Impedance: Sketch a circuit and phasor diagram; mangnitude of voltage, impedance; power supplied, total current

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    Only need questions 4, 5, and 6.

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    Please see the attached file.

    Resonance is achieved when the impedance of the circuit is purely ohmic. This means that the reactivity of the capacitor has the same magnitude as the inductor reactivity (since they have opposite direction in the phasor diagram, they will cancel each other out).
    Thus the phasor diagrams for resonance will look like:

    Hence in resonance the frequency is:

    Which gives:

    The angular frequency is simply:

    In ...

    Solution Summary

    The detailed explanations to each of the problems include diagrams and calculations.