How to use inductors and capacitors to increase power through resistor?

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i'm given a circuit that contains a 15 volt battery and a resistor that has a power rating of 1/4 watt and a resistance that must be greater than 1 kohm. i'm told that no matter how i set it up, i cannot exceed the 1/4 watt power rating of the resistor. this makes sense. i work out the max power using P = IV and get 0.225 watts. however, the problem then asks me to add capacitors and inductors to the circuit such that the resistor's power rating is exceeded. how would i use capacitors and inductors to do this?

i don't really want an explicit answer but would really appreciate help with the general idea of how this could be done. we haven't covered this but it's on the hw.
 

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ehild
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In an AC circuit, the voltage across the resistor can exceed that of the voltage source. Remember that the AC voltage near resonance can be very high with respect to the source voltage. If you have the resistor connected parallel to a reactive element, the voltage across it can be higher than the source voltage or the allowed voltage.

Try a circuit with an inductor in series with the resistor connected parallel with a capacitor. Find the condition needed that the power of the circuit exceed the nominal power rating of the resistor.

As an example, determine the power when the angular frequency of the 15 V source is ω=1000 1/s and a 2 μF capacitor is connected parallel to the 1kΩ resistor, and they together are in series with a 0.5 H inductor.

ehild
 
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