A hair dryer has a power rating of 1200 W at 120 V rms. Assume the hair dryer circuit contains o

A hair dryer has a power rating of 1200 W at 120 V rms....

A hair dryer has a power rating of $1200 \mathrm{W}$ at $120 \mathrm{V}$ rms. Assume the hair dryer circuit contains only resistance. (a) What is the resistance of the heating element? (b) What is the rms current drawn by the hair dryer? (c) What is the maximum instantaneous power dissipated?

A hair dryer has a power rating of $1200 \mathrm{W}$ at $120 \mathrm{V}$ rms. Assume the hair dryer circuit contains only resistance.
(a) What is the resistance of the heating element?
(b) What is the rms current drawn by the hair dryer?
(c) What is the maximum instantaneous power dissipated?

Key Concepts

Power Calculations in Resistive Loads

In a resistive circuit, power can be calculated using the formula P = V²/R or P = I²R, where P is the power, V is the voltage, and I is the current. These relationships allow the determination of the resistance required for a given power rating or the current drawn by the load. They also help in understanding how instantaneous power can be expressed, especially in the context of sinusoidal AC signals.

RMS Values in AC Circuits

RMS, or root-mean-square, values are used in AC circuits to represent equivalent steady DC values for voltage and current. Since AC quantities vary with time, RMS values provide a means to calculate average power dissipation in resistive components, making them essential for practical power calculations.

Ohm's Law

Ohm's law states that the voltage across a resistor is directly proportional to the current flowing through it, with the constant of proportionality being the resistance (V = IR). This fundamental relation is key to determining any one of the three variables—voltage, current, or resistance—when the other two are known.

Resistive Circuit Analysis

This concept involves understanding that in a circuit containing only resistive elements, the relationships between voltage, current, and power are governed by linear equations. The analysis primarily uses Ohm's law and power formulas, avoiding complications like phase shifts or reactance that arise in circuits with inductors or capacitors.

Transcript

00:01 High in the given problem power rating of the hair dryer is given as p average is equal to 1200 watt rms voltage fed to this hair dryer is 120 volt so in the first part of the problem we have to find the resistance of this hair dryer so using the expression for average power dissipated in the hair dryer which is given as the product of rms voltage with the rms current and with the power factor.

00:54 But for a circuit having resistance only the power factor comes out to be one.

01:03 So this average power consumed may also be given as the product of rms voltage and for rms current we can use hom's law using which this irms is given as vrms divided by r means resistance of the air dryer so it becomes square of rms voltage with the resistance divided by the resistance so an expression for the resistance of the hair dryer here comes out to be the ratio of rms square of rms voltage with the average power consumed hence this resistance will be given as the square of 120 divided by twelve hundred so finally resistance of this hair dryer comes out to be twelve which becomes the answer for the first part of this problem resistance of the hair dryer.

02:20 Now in the second part of the problem we have to find the average current first of all rms current and that rms current will be given by again using the same expression here as we have used earlier p average is equal to vrms into i rm s into i r r r r r r so irms will be given by the ratio of average power consumed with the rms voltage applied.

02:49 So this is 1200 watt divided by 120 volt.

02:57 So rms current in this hair dryer comes out to be 10 ampere which is the answer for the second part of this problem...

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