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I have a resistor and an inductor in parallel, picture included and I want to calculate the reactive and true power given a voltage U. This is my solution but its not correct.
\(Z = \frac{Z_4Z_5}{Z_4+Z_5} = \frac{R_2\omega ^2L_2^2}{R_2^2+\omega ^2L_2^2} + j\frac{R_2^2\omega L_2}{R_2^2+\omega ^2L_2^2} = R + jX\)
The complex power is equal to.
\(S = \frac{UI^*}{2}\)
\(I = \frac{U}{Z} = \frac{UZ^*}{ZZ^*}\)
\(\Rightarrow S = \frac{UU^* Z^*}{ZZ^*} = \frac{|U|^2(R-jX)}{R^2+X^2}\)
This now gives the true and reactive power, P and Q respectivley
\(P = real(S)\)
\(Q = imag(S)\)
Thanks for any help
\(Z = \frac{Z_4Z_5}{Z_4+Z_5} = \frac{R_2\omega ^2L_2^2}{R_2^2+\omega ^2L_2^2} + j\frac{R_2^2\omega L_2}{R_2^2+\omega ^2L_2^2} = R + jX\)
The complex power is equal to.
\(S = \frac{UI^*}{2}\)
\(I = \frac{U}{Z} = \frac{UZ^*}{ZZ^*}\)
\(\Rightarrow S = \frac{UU^* Z^*}{ZZ^*} = \frac{|U|^2(R-jX)}{R^2+X^2}\)
This now gives the true and reactive power, P and Q respectivley
\(P = real(S)\)
\(Q = imag(S)\)
Thanks for any help
