Compute the rms values of the electric current and voltage

Question

Question 1. The electric current and voltage at one terminal of a single phase transmission line are:

I^~ = 141cos(ωt - 10^o),A

V^~ = 390cos(ωt + 5^o),V

Compute the rms values of the electric current and voltage, the complex power, and the real and reactive power flowing into the line.

Question 2. Two single-phase ideal voltage sources are connected by a line of impedance of 0.7 + j2.4 Ω as shown in Fig. V₁ = 500⌊16.26^o V and V₂ = 585⌊0^o V.  Plot V'₁ V'₂, and I'₁₂ in a phasor diagram. Also, find the real and reactive power loss in the line.

Question 3. A single-phase inductive load consisting of R and X in series feeding from a 2400-V rms single-phase supply absorbs 288 kW at a lagging power factor of 0.8. Determine R and X.

Question 4. The system shown in Fig. is balanced. Assume that:

Z = 10⌊-15^o Ω

V_ca = 208⌊-120^o V

Find V_ab, V_bc V_an V_bn V_cn, I_a, I_b and I_c

Question 5. A balanced delta-connected load consisting of a pure resistances of 18Ω per phase is in parallel with a purely resistive balanced Y-connected load of 12Ω per phase as shown in Fig. 3.

The combination is connected to a three-phase balanced supply of 346.41-V rms (line-to-line) via a three-phase line having an inductive reactance of 3 j Ω per phase. Taking the phase voltage an V as reference, determine

(a) The magnitudes of current, real power, and reactive power drawn from the supply.

(b) The line-to-neutral and the line-to-line voltage magnitudes of phase a at the combined load terminals.