Finding power in a simple AC circuit

Question

I am trying to find power in this circuit.

^{simulate this circuit – Schematic created using CircuitLab}

I have calculated this multiple ways and I keep getting the same answer

R Parallel = 3.846-j0.769Ohm

R total = 3.846+j2.23Ohm

I total = 7/(3.846+j2.23) = 1.36 - j0.7898Amp

P Source Avg = (((7)(1.36-j0.7898))/2)cos(-30) = 4.76Watt

Using node to find Va:

((1/j3)+.25+(1/(-j20)))Va - (7/(j3)) = 0

Va = 4.63-j4.086 Volts

Va/4 = 1.157-j1.021Amps = (1.543<-41 degree)Amps

Power 4Ohm Avg = (((1.543)(1.543)(4))/2)cos(-41) = 3.594 Watt

or using loop

(4+j3)I1 - 4I2 +7 = 0

And

(4-j20)I2 - 4I1 = 0

4(I2 - I1) = 1.158 - j1.021

This is the moment I realised I have the correct answer using loop already written down

I am still unsure what is wrong with my node approach

((1.573*7)/2)cos(149) = -4.7182 Watt

Power average supplied by the source is: 4.76w

Power through the resistor is: 3.594w

Now I am reasonably confident in my answer but it does not make sense. Because the average power through an inductor and a capacitor is 0 shouldn't the power from the source and the power absorbed by the resistor be the same amount?

Answer 1

The power delivered by the source should exactly match the power dissipated by the resistor but this is only true once the circuit has settled down.

From a transient point of view energy is shipped out from the source and that energy produces heat in the resistor but also "charges" the reactive components.

This means that initially more power is taken from the source but, after the transient has settled down, the power in the resistor IS the power delivered by the source.

You have made a mistake but, you haven't shown your workings.