Chapter 18, Problem 64GP

(a)

To determine

The change percentage in the output power.

Answer to Problem 64GP

The answer is $19.5\%decrease$ .

Explanation of Solution

Given:

Dryer designed for Voltage, $117V$

Voltage drops by $105V$

Formula used:

By the definition of the power, $P=VI$

Where, $P$ is power, $V$ is voltage and $I$ is current.

Using Ohm’s law, electrical power will be $P=\frac{V^2}{R}$

Where, $V$ is voltage, $I$ is current and $R$ is resistance.

Calculation:

By using the formula of electrical power:

  $\begin{array}{l}P=\frac{V^2}{R}=\frac{P_{105}}{P_{117}}\\ =\frac{\frac{{\left(105V\right)}^2}{R}}{\frac{{\left(117V\right)}^2}{R}}\\ =\frac{{\left(105V\right)}^2}{{\left(117V\right)}^2}\\ =19.5\%decrease\end{array}$

Conclusion:

The change is $19.5\%decrease$

(b)

To determine

To explain: The effect on the answer obtained in part (a) with actual change in resistivity with temperature.

Answer to Problem 64GP

When the temperature increases, then the relaxation time will decrease. So, the ratio of resistivity and conductivity will increase respectively.

Explanation of Solution

Given:

Dryer designed for Voltage, $117V$

Voltage drops by $105V$

The change percentage in the output power: $19.5\%decrease$

Formula used:

It is known that resistance:

  $R=\frac{\rho L}{A}$

Where,

  $\rho$ is the resistivity.

  $L$ is the length of wire

  $A$ is the cross-sectional area of the wire.

Calculation:

Now, assume the resistance wire to follow pattern metals do when heating up, resistance of hair dryer will change according to the temperature change.

So, when the temperature will increase, the resistance will also increase. Also, when the temperature will decrease, power supplied would be higher than part a.

Conclusion: The actual change in resistivity with temperature will affect the answer.