Question

Thermal energy is produced in a resistor at a rate of 100Wwhen the current is 3.00 A.What is the resistance?

Short answer

The resistance value is $11.1\Omega$.

Step-by-step solution

Identification of given data

a) The rate of production of thermal energy is$P=100W$

b) The current flowing is $I=3.00A$.

Significance of the power

The power or rate of energy transfer, in an electrical device across which a potential difference is equal to the product of current and potential difference. It can also be defined as energy transferred per unit time.

We need to use the formula for power (resistive dissipation) relating to current and resistance to find the resistance of a resistor.

Formulae:

The power produced during energy dissipation,$P=I^{2}R$ …(i)

Here,P is the power,I is current,R is resistance.

Determining the resistance

Using the given data in the formula of dissipated power of equation (i), we can get the value of the resistance as follows:

$$\begin{gathered} R=\frac{P}{I^2} \\ =\frac{100W}{{\left(3.00A\right)}^2} \\ =11.1\Omega \end{gathered}$$

Hence, the value of the resistance is $11.1\Omega$.