31. Alternating Current
RMS Current and Voltage
7PRACTICE PROBLEM
A student is designing a prototype for a three-phase power system. The system consists of three parallel wires, A, B, and C, carrying currents. The emfs generating the currents are ε A = (12 V) cos(ωt), ε B = (12 V) cos(ωt + 2π/3), and ε C = (12 V) cos(ωt - 2π/3) where 12 V represents the peak voltage. The power associated with the emfs and transmitted by the three wires is 120 W. Calculate the rms current in each wire if each of these wires supplies one-third of the total power.
A student is designing a prototype for a three-phase power system. The system consists of three parallel wires, A, B, and C, carrying currents. The emfs generating the currents are ε A = (12 V) cos(ωt), ε B = (12 V) cos(ωt + 2π/3), and ε C = (12 V) cos(ωt - 2π/3) where 12 V represents the peak voltage. The power associated with the emfs and transmitted by the three wires is 120 W. Calculate the rms current in each wire if each of these wires supplies one-third of the total power.