Question

part b
estimate the resistance of the 120 - v$_{rms}$ circuits in your house as seen by the power company, when there are two 90 w lightbulbs burning. express your answer to two significant figures and include the appropriate units.
r = value units

Explanation:

Step1: Calculate total power

The power of each light - bulb is $P_1 = 90\ W$, and there are two light - bulbs. So the total power $P=P_1 + P_2=90\ W+90\ W = 180\ W$.

Step2: Use power - voltage - resistance formula

The formula for power in an AC - DC equivalent circuit is $P=\frac{V_{rms}^2}{R}$, where $V_{rms}=120\ V$ and $P = 180\ W$. We can re - arrange the formula to solve for resistance $R$. So $R=\frac{V_{rms}^2}{P}$.

Step3: Substitute values and calculate

Substitute $V_{rms}=120\ V$ and $P = 180\ W$ into the formula $R=\frac{V_{rms}^2}{P}=\frac{120^2}{180}=\frac{14400}{180}=80\ \Omega$.

Answer:

$80\ \Omega$