Question

part a
estimate the resistance of the 120 - vrms circuits in your house as seen by the power company, when everything electrical is unplugged
the resistance is zero.
the resistance is infinite.
there is not enough information to answer.
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part b
estimate the resistance of the 120 - vrms circuits in your house as seen by the power company, when there are two 60 w lightbulbs burning
express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Calculate the resistance of one light - bulb

The power formula is \(P=\frac{V^{2}}{R}\), where \(P = 60\space W\) and \(V=120\space V\). Rearranging for \(R\), we get \(R=\frac{V^{2}}{P}\).
Substituting the values: \(R=\frac{(120)^{2}}{60}=240\space\Omega\)

Step2: Calculate the equivalent resistance of two light - bulbs in parallel

For two resistors \(R_1 = R_2=240\space\Omega\) in parallel, the equivalent resistance formula is \(R_{eq}=\frac{R_1\times R_2}{R_1 + R_2}\)
Substituting \(R_1 = R_2 = 240\space\Omega\): \(R_{eq}=\frac{240\times240}{240 + 240}=\frac{240\times240}{480}=120\space\Omega\)

Answer:

\(120\space\Omega\)