Question

a hair - dryer draws 15.5 a when plugged into a 120 - v line. assume direct current. what is its resistance? express your answer to two significant figures and include the appropriate units. part b how much charge passes through it in 19 min? express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Find resistance using Ohm's law

According to Ohm's law $V = IR$, where $V$ is voltage, $I$ is current and $R$ is resistance. We can solve for $R$, so $R=\frac{V}{I}$. Given $V = 120\ V$ and $I=15.5\ A$. Then $R=\frac{120}{15.5}\ \Omega$.
$R=\frac{120}{15.5}\approx7.7419\ \Omega$. Rounding to two - significant figures, $R = 7.7\ \Omega$.

Step2: Find charge using $Q = It$

The current $I = 15.5\ A$ and the time $t=19\ min$. First convert time to seconds, since $1\ min = 60\ s$, then $t = 19\times60\ s=1140\ s$.
Using the formula $Q = It$, we substitute $I = 15.5\ A$ and $t = 1140\ s$. So $Q=15.5\times1140\ C$.
$Q = 17670\ C$. Rounding to two - significant figures, $Q = 1.8\times10^{4}\ C$.

Answer:

Part A:
$R = 7.7\ \Omega$
Part B:
$Q = 1.8\times10^{4}\ C$