Question

A hair dryer is treated as a pure resistor. But because there are coils in the heating element and in the motor that drives the blower fan, a hair dryer also has inductance. Qualitatively, does including an inductance increase or decrease the values of $\mathrm{R},{\mathrm{l}}_{\mathrm{rms}},\mathrm{and}\mathrm{P}$?

Short answer

The resistance is unaffected while both $l_{rms}andP$will decrease upon including the inductance

Step-by-step solution

Given Data

An inductor is a passive two-terminal device that stores energy in a magnetic field when current passes through it. When an inductor is attached to an AC supply, the resistance produced by it is called inductive reactance$\left({\mathrm{X}}_{\mathrm{L}}\right)$.

Resistance is measure of opposition to the flow of current in a closed electrical circuit. It is measured in Ohm (Ω).

Impedance is defined as the effective resistance of an electric circuit to the flow of current due to the combined effect of resistance (offered by resistor) and reactance (offered by capacitor and inductor).

Effect of Inductance

The net impedance of the hair dryer to the flow of current due to presence of inductance and resistance:

$Z=\sqrt{R^2+{X_L}^2}$

The rms value of current can be given by

$I_{rms}=V/Z$

The power is given by

$P=I_{rms}V\cos \varphi$

As the resistance value is not dependent on inductance, its value will not be affected but the overall impedance of the circuit will increase by including inductance. Also, rms current is inversely proportional to impedance which means its value will decrease and since power consumed is directly proportional to rms current, its value will also decrease.

Therefore, the resistance is unaffected while both $I_{rms}andP$will decrease upon including the inductance.