Final answer:
The active power in the AC circuit is 1 kW and the reactive power is 1000 VAR, calculated using the real and imaginary components of the given voltage and current.
Step-by-step explanation:
The student is asking about calculating the active and reactive power in an AC circuit where the voltage (V) is (100+j200)V and the current (I) is (10+j5)A. The active power (P) can be calculated by multiplying the real parts of V and I, and the reactive power (Q) can be calculated by multiplying the imaginary parts of V and I and then taking the difference between the two products if they have opposite signs or adding them if they have the same signs.
For the active power: P = Re(V) × Re(I) = 100 V × 10 A = 1000 W or 1 kW.
For the reactive power: Q = Im(V) × Im(I) = 200 V × 5 A = 1000 VAR (Volt Amperes Reactive).
Therefore, the active power dissipated is 1 kW, and the reactive power in the circuit is 1000 VAR.