Chapter 22, Problem 9STP

To determine

To calculate: The current in the given circuit. Also the energy used by the hair dryer for the given time.

Answer to Problem 9STP

The current through the circuit is $14.12\text{ A}$

The energy used by the hair dryer is $\text{2}\text{.54}\times {10}^5\text{ J}$

Explanation of Solution

Given:

A DC generator circuit with a hair dryer as load with resistance $8.5\Omega$ , is used for duration of 2.5 min.

Formula used:

Given the resistance of the circuit and supply voltage, the current can be calculated using the Ohm’s law as,

  $\begin{array}{l}V=IR\\ I=\frac{V}{R}\end{array}$........(1)

The energy consumed by the resistance, E can be expressed in terms of the power dissipation and the time for which power is drawn, t, as

  $E=Pt$

Here, the power drawn by the resistance is a function of current I and voltage drop across it, V, which can be expressed as,

  $P=VI$

Calculation:

Consider the circuit shown in Figure 1. Here, the DC generator is supplying a voltage of 120 V and is loaded with a hair dryer of 8.5 Ω resistance. The current through the dryer can be calculated by using the relation in (1), as

  $\begin{array}{c}I=\frac{120}{8.5}\\ =14.12\text{ A}\end{array}$

  

Figure 1

Substituting the voltage and current value, the power can be obtained as,

  $\begin{array}{c}P=120\times 14.12\\ =1.69\times {\text{10}}^3\text{ W}\end{array}$

Now, substituting the value of power and time, the energy can be calculated as,

  $\begin{array}{c}E=1.69\times {10}^3\times 2.5\times 60\\ =2.54\times {10}^5\text{ W/s}\\ =\text{2}\text{.54}\times {10}^5\text{ J}\end{array}$

Conclusion:

Therefore, the current through the circuit is 14.12 A and the energy absorbed by the hair dryer is $\text{2}\text{.54}\times {10}^5\text{ J}$ .