AC Power Accounting

Let P R P_R be the combined power (in watts) consumed by all of the resistors in the circuit. Let P 1 P_1 be the power (in watts) supplied by ideal voltage source V 1 V_1 to the rest of the circuit.

What is P 1 P R \large{\frac{P_1}{P_R}} ?

Details:
1) Voltage magnitudes ( V 1 , V 2 , V 3 , V 4 ) = ( 15 , 10 , 12 , 15 ) (V_1, V_2, V_3, V_4) = (15, 10, 12, 15) . All voltage source phase angles equal

Hint: If the voltage of the source is V 1 V_1 and the current flowing out of the source is I 1 I_1 , the active power flowing out of the source is R e [ V 1 I 1 ] Re[V_1 \, I_1^*] , where the " * " symbol denotes the complex conjugate of the current. If we calculate the powers flowing out of all sources and add them up, how does the sum compare to the total power consumed by the resistors?


The answer is 1.1538.

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