Question

what is wattless current?prove that an ideal capacitor in an AC circuit does not dissipat power?​

Answer 1

The power is a circuit is measured in watts and is equal to the voltage times the current. If you apply a d.c. voltage to a resistor then you will dissipate a certain amount of energy (watts) which appears as heat. This wattage figure will be the same at any instant in time.

If you apply an a.c. voltage to a resistor you will get a similar situation but the voltage and current will rise and fall together so the instantaneous watts varies from zero to a peak. This averages over a cycle which we quote as the rms voltage , current and power.

when volts is +ve the current is +ve then volts * current gives a +ve watts

when volts is -ve the current is -ve then volts * current gives a +ve watts

so, the watts in a resistor is always positive - it always dissipates heat and never absorbs it instead.

When you apply an a.c. voltage to Inductors and capacitors you get a somewhat curious result. The current in the inductor (or capacitor) will not be in phase with the voltage applied. When you do your calculations of the power at instants through the cycle there are times when the result shows that the watts is negative - because the voltage is positve when the current is negative or vice versa).

So, we can have a circuit where at some instants the power dissipated or consumed is +ve and at some instants it is -ve. Add these +ve and -ve amounts up over a cycle and you can get a wattage figure that is very close to zero even though a lot of current has been flowing. The explanation for how this can be so is that inductors store energy in their magnetic field at some instants and release it again at others Capacitors are similar but their field is an electric field not magnetic.

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