Final answer:
The power rating required for the inverter with a power factor of 0.7 to support loads consuming 306 W, 220 W, and 156 W should be approximately 974.29 VA.
Step-by-step explanation:
The question involves calculating the power rating in volt-amperes (VA) of an inverter given the power consumption of three parallel loads and the power factor of the inverter. The power factor is a measure of how effectively electrical power is converted into useful work output, and it is less than 1 for most systems. The total real power consumed by the loads is the sum of the power of each load, which is 306 W + 220 W + 156 W = 682 W. Given the power factor of 0.7, the apparent power (S) in VA required by the inverter can be calculated using the formula S = P / power factor, where P is the total power consumption.
Therefore, the required power rating of the inverter is S = 682 W / 0.7 ≈ 974.29 VA. Hence, the inverter should be rated at least 974.29 VA to support the given system.