Question

A hair dryer draws 9.0 A when plugged into a 120-V line. (a) What is its resistance? (b) How much charge passes through it in 15 min?

Answer 1

Given:

The current drawn by the hair dryer is: I = 9 A

The voltage applied to the hair dryer is: V = 120 v

The time for which the charge passes is: t = 15 min = 15 × 60 s = 900 s

To find:

a) The resistance

b) Charge passing through the resistor in 15 mins

Explanation:

a)

The expression for potential difference (V) in terms of current (I) and resistance (R) is given as:

$V=IR$

Rearranging the above equation, we get:

$R=\frac{V}{I}$

Substituting the values in the above equation, we get:

$\begin{gathered} R=\frac{120\text{ v}}{9\text{ A}} \\ \\ R=13.33\text{ }\Omega \end{gathered}$

b)

The electric current (I) through the conductor is defined as the amount of charge (Q) passing through the conductor per unit time (t). It is given as:

$I=\frac{Q}{t}$

Rearranging the above equation and substituting the values in it, we get:

$Q=It=9\text{ A}\times900\text{ s}=8100\text{ C}$

Final answer:

a) The resistance is 13.33 Ω

b) The charge passing for 15 mins is 8100 C.