A typical american family uses 1000 kwh of electricity pro 30 days.

Asked by wiki @ 29/10/2020 in Physics viewed by 399 People

What is the average rms current in the 120 V power line to the house?

On average, what is the resistance of a household?

Answered by wiki @ 29/10/2020

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

$V_{rms}=\frac{V_p}{\sqrt{2}}=\frac{120 V}{\sqrt{2}}=84.9 V$

The family uses 1000 kWh of energy per month. Since

1 kW = 1000 W

1 h = 3600 s

This energy corresponds to

$E=1000 kWh \cdot (1000 W/kW)\cdot (3600 s/h)=3.6\cdot 10^9 Ws=3.6\cdot 10^9 J$

The time interval considered is 1 month, which corresponds to

$t=1 m = (30 d)(24 h)(60 min)(60 s)=2.6\cdot 10^6 s$

And the power is the ratio between the energy used and the time taken:

$P=\frac{E}{t}=\frac{3.6\cdot 10^9 J}{2.6\cdot 10^6 s}=1385 W$

And now we can find the average rms current by using the relationship between power, voltage and current:

$I_{rms}=\frac{P}{V_{rms}}=\frac{1385 W}{84.9 V}=16.3 A$

2. $5.2 \Omega$

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

$R=\frac{V_{rms}}{I_{rms}}=\frac{84.9 V}{16.3 A}=5.2 \Omega$

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