Question

A hair dryer draws 6.2 when plugged into a 120 V-line.What is its resistance?How much charge passes through it in 10min ? (Assume direct current.)

Answer 1

Concepts and reason

The main concepts required to solve this problem are the charge, current and time.

Initially, write the equation for the current passing through the conductor per unit time and Ohm’s law. Use these equations and first calculate the resistance and then calculate the charge passes through the hair dryer.

Fundamentals

The equation for the Ohm’s law is,

$V = IR$

Here, V is the potential difference, I is the current and R is the resistance.

The equation for the current through the conductor per unit time is,

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

Here, Q is the charge passing through the conductor and t is time taken to pass the charge through the conductor.

The equation for the Ohm’s law is,

$V = IR$

Here, I is the current passing through the hair dryer, and R is the resistance of the hair dryer.

Rearrange the above equation for R.

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

Substitute 120 V for R, and 6.2 A for I in above equation.

$\begin{array}{c}\\R = \frac{{120{\rm{ V}}}}{{6.2{\rm{ A}}}}\\\\ = 19.35\,{\rm{ V/A}}\,\left( {\frac{{1\,\Omega }}{{1{\rm{V/A}}}}} \right)\\\\ = 19.35\,\Omega {\rm{ }}\\\end{array}$

The equation for the current passing through the hair dryer is,

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

Here, Q is the charge of the hair dryer and t is the time.

Rearrange the above equation for Q.

$Q = It$

Substitute 6.2 A for I and 10 min for t in above equation.

$\begin{array}{c}\\Q = \left( {6.2{\rm{ A}}} \right)\left( {10{\rm{ min}}\left( {\frac{{60{\rm{ s}}}}{{1{\rm{ min}}}}} \right)} \right)\\\\ = 3720\,{\rm{A}} \cdot {\rm{s}}\left( {\frac{{1{\rm{ C}}}}{{{\rm{A}} \cdot {\rm{s}}}}} \right)\\\\ = 3720{\rm{ C}}\\\end{array}$

Ans:

The resistance of the hair dryer is $19.35\,\Omega {\rm{ }}$ .

The amount of charge passing through the hair dryer is 3720 C.