Question

A 60-cm-long heating wire is connected to a 120 V outlet. If the wire dissipates 45 W, what are (a) the current in and (b) the resistance of the wire?

Answer 1

Concepts and reason

The concepts required to solve the given problem are ohms law and power.

Initially, calculate the current in the wire by using the relation between power, voltage, and current. Finally, calculate the resistance of the wire by using ohms law.

Fundamentals

According to ohm’s law, the current passing through the conductor is directly proportional to the voltage.

$V = IR$

Here, V is the voltage, I is the current, and R is the resistance.

The rate of electrical energy dissipated is called as power.

The expression for the power is,

$P = \frac{E}{t}$

Here, E is the electrical energy and t is the time.

The expression for the electrical energy is,

$E = VIt$

(a)

The expression for the power is,

$P = VI$

Rearrange the above equation for the current.

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

Substitute 45 W for P and 120 V for V.

$\begin{array}{c}\\I = \frac{{45\;{\rm{W}}}}{{120\;{\rm{V}}}}\\\\ = 0.375\;{\rm{A}}\\\end{array}$

(b)

From the ohms law, the voltage is,

$V = IR$

Rearrange the above equation for the resistance.

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

Substitute 120 V for V and 0.375 A for I.

$\begin{array}{c}\\R = \frac{{120\;{\rm{V}}}}{{0.375\;{\rm{A}}}}\\\\ = 320\;\Omega \\\end{array}$

Ans: Part a

The current in the wire is 0.375 A.

Part b

The resistance of the wire is $320\;\Omega$ .