Question

A resistor with a potential difference of 200 V across it transfers electrical energy to thermal energy at the rate of300 V. What is the resistance of the resistor?

Short answer

The resistance of the resistor is $13.3\mathrm{\Omega }$.

Step-by-step solution

The given data:

A potential difference of the resistor, V = 200 V

Rate of transfer of electrical energy to thermal energy, P = 3000 W

Understanding the concept of resistance:

From the relationship between power, potential, and resistance, the resistance is inversely proportional to power and directly proportional to the square of potential. Using this you can calculate the resistance.

Formula:

The electric power generated in the circuit,

$$\begin{gathered} \mathrm{P}=\frac{{\mathrm{V}}^2}{\mathrm{R}} \\ \left(1\right)\mathrm{R} \end{gathered}$$ ….. (1)

Here, P is the electric power, V is the potential, and R is the resistance.

Calculation of the resistance:

Resistance is the property of the material that resists the flow of charges.

By substituting the given values in equation (1), you can get the value of the resistance as follows:

$$\begin{gathered} \mathrm{R}=\frac{{\mathrm{V}}^2}{\mathrm{P}} \\ =\frac{{\left(200\right)}^2}{3000} \\ =13.3\mathrm{\Omega } \end{gathered}$$

Hence, the value of the resistance is $13.3\mathrm{\Omega }$.