Physics, 22.12.2019 04:31 maya7544

Atypical american family uses 1000 kwh of electricity a month.

what is the average rms current in the 120 v power line to the house?

on average, what is the resistance of a household?

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Answer from: lareynademividp0a99r

The average rms current in the power line to the house is 12AThe average resistance of a household is 10Ω.

Given the data in the question;

Electricity used; E = 1000kWh = 36*10^8J

Time; t = 1 month = 2.592 * 10^6s

Voltage; V = 120V

Calculate the average rms current to the house.

First we determine the power

Power is the amount of energy transferred per unit time:

$Power = \frac{E}{t}$

So we substitute in our values

$Power = \frac{36*10^8J}{2.592*10^6s}\\\\Power = 1.388 * 10^3 J/s \\\\Power = 1.388 * 10^3 W$

Next we Calculate the Current

From Ohms Law:

P = I * V

We substitute in our values

$1.388*10^3W = I \ *\ 120V \\\\I = \frac{1.388*10^3W}{120V} \\\\I = 11.57 W/V\\\\I = 12A$

Therefore, the average rms current in the power line to the house is 12A

The resistance of a household

From Ohm's Law:

$R = \frac{V}{I}$

We substitute in our values

$R = \frac{120V}{12A}\\\\R = 10ohms$

Therefore, The average resistance of a household is 10Ω.

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Answer from: lashayl27

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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Atypical american family uses 1000 kwh of electricity a month.

what is the average rms c...