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Suppose we were told that 100V (100j0V) RMS was applied to this circuit how
much current will flow?

We have 100j0V (we don't know the frequency, but we do know the complex
impedance) applied across 7-j10.95Ω.
I=E/Z=(100j0)/(7-j10.95)

Using the calculator again, I get. I=4.1444+j6.4830 amperes

I get a complex current because there is reactance in the circuit. I could easily (with
a calculator or by hand, but why do it by hand) convert this to polar and I would get
the magnitude and phase angle of the current.

I=7.6945/57.4105°A

[note: We could have used the magnitude of the total impedance to find the
magnitude of the total current i.e. I=E/Z = 100/12.996 =7.694A
We have nearly 7.7 amperes but there is a phase shi� between current and voltage
of approximately 57.4°.

What if we calculated the power dissipated or radiated by the circuit by the applied
voltage and the magnitude of the impedance?

We have 100V RMS with 7.6945A flowing.
2
P=l Z
2
P=(7.6945) x12.996=796 wa�s* (Or is it!. This is wrong.)
2
Or we could have done the same thing using P=E /Z
2
P=(100) /12.996 = 796 wa�s!*(s�ll wrong)

This cannot be the true power dissipated in the circuit because the circuit has
reactance. We call this the apparent power and it is measured in VA (volt-amperes)
*The power we calculated here is the apparent power in volt-amperes (VA) not wa�s.
We know there is 7.6945/57.4105°A flowing in the circuit. This current flows through
all components in a series circuit. So, this is the current flowing through our R, which
is 7Ω.

What if we calculated the power dissipated (or radiated) in R?

P=I R
2
2
P=(7.6945) x7Ω = 414.4373W ≈ 414W
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