1. What is the average RMS current in the 120 V power line to the house?
2. On average, what is the resistance of a household?
1. 16.3 A
To calculate the average RMS current, we have to calculate the average RMS current first. The peak voltage of the power line is Vp = 120 V, so the RMS voltage is
The family uses 1000 kWh of energy per month. Since
1 kW = 1000 W
1 h = 3600 s
This energy corresponds to
The time interval considered is 1 month, which corresponds to
And the power is the ratio between the energy used and the time taken:
And now we can find the average RMS current by using the relationship between power, voltage, and current:
The average resistance of the household can be calculated by using Ohm’s law. Using the value found for the RMS voltage and the RMS current, we find
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