Question

How much electrical energy is transferred to thermal energy in 2.00hby an electrical resistance of$\mathbf{400}\mathbf{\Omega }$when the potential applied across it is 90.0V?

Short answer

Electrical energy transferred to the thermal energy is $1.46\times {10}^5\mathrm{J}$.

Step-by-step solution

The given data

a) Applied potential difference,$V=90.0V$

b) Resistance value,$R=400\Omega$

c) Time taken to transfer the energy,$t=2hor7200s$

Understanding the concept of the energy

We know the relation between power and potential. From this relation, we calculate total power. Using this power, we can calculate the total time in seconds and find the energy transferred to the thermal energy.

Formulae:

The electrical power due to the applied potential difference,$P=\frac{V^2}{R}$ (i)

The energy transferred by the system, $E=Pt$ (ii)

Calculation of the transferred electrical energy

Using the given data in equation (i), we can get the electrical power or the rate of energy transfer as follows:

$$\begin{gathered} P=\frac{{90}^2}{400} \\ =\frac{8100}{400} \\ =20.3\mathrm{J}/\mathrm{s} \end{gathered}$$

Now, we can get the value of the electrical energy transferred to the thermal energy using the given data in equation (ii) as follows:

$$\begin{gathered} E=20.3\times 7200 \\ =1.46\times {10}^5\mathrm{J} \end{gathered}$$

Hence, the value of the energy transferred is $1.46\times {10}^{5}J$.