What is the resistance of a$1500W\left(120V\right)$ hair dryer? What is the current in the hair dryer when it is used?

We have given that $1500W\left(120V\right)$.

We need to find the resistance of a hair dryer and the current in the hair dryer when it is used.

When the current flows through a resistor, the energy is dissipated, the rate of the dissipated energy is the power. This rate where the energy is transferred from the current to the resistor is

$P_R=I∆V_R...\left(1\right)$

From Ohm's law $∆V_R=IR$, we can get an alternative formula

$P_R=I∆V_R=I^{2}R=\frac{{(∆V_R)}^2}{R}...\left(2\right)$

The formula ${(∆V_R)}^2/R$shows the largest dissipated power if we have several resistors. Solve equation (2) for $R$which is our target to be in the form

$R=\frac{{(∆V_R)}^2}{P_R}...\left(3\right)$

Now, putting the values of$P_R$and $∆V_R$into equation (3) to get $R$by

$$\begin{gathered} R=\frac{{(∆V_R)}^2}{P_R} \\ =\frac{{\left(120V\right)}^2}{1500W} \\ =9.6\Omega \end{gathered}$$

For the current, solving equation (1) to be in the form

$I=\frac{P_R}{∆V_R}...\left(4\right)$

Now we plug the values for $P_R$and $∆V_R$into equation (4) to get $I$by

$$\begin{gathered} I=\frac{P_R}{∆V_R} \\ =\frac{1500W}{120V} \\ I=12.5A \end{gathered}$$