Exams › GATE › Engineering Mathematics

An AC source of RMS voltage 20 V with internal impedance Zs = (1 + 2j) Ω feeds a load of impedance ZL = (7 + 4j) Ω in the figure below. The reactive power consumed by the load is

1. 8 VAR
2. 16 VAR
3. 28 VAR
4. 32 VAR

Correct answer: 16 VAR

Solution

Total impedance = Zs + ZL = (1+2j)+(7+4j) = 8+6j, |Z| = 10 ohm. RMS current |I| = 20/10 = 2 A. Reactive power in the load = |I|^2 * X_L = 4 * 4 = 16 VAR, not 32 VAR.

Related GATE Engineering Mathematics questions

• z = (2 - 3i)/(-5 + i) can be expressed as
• If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral ∫_D 1/(s² - 1) ds is
• The equation sin(z) = 10 has
• The residue of the function f(z) = 1 / ((z + 2)² (z - 2)²) at z = 2 is
• If f(z)=c₀+c₁ z⁻¹, then ∮ (1+f(z))/z dz is given by unit circle
• The residues of a complex function X(z)=(1-2z)/(z(z-1)(z-2)) at its poles are

⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →