A 1250 Wradiant heater is constructed to operate at 115 V. (a) What is the current in the heater when the unit is operating? (b) What is the resistance of the heating coil? (c) How much thermal energy is produced in 1.0 h?

1. The power dissipated is P = 1250W.
2. The potential difference is V = 115V.
3. The time of energy production is t = 1.0h or 3600s.

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.

By using the equation for the rate of electrical energy transferred, Ohm’s law, and the thermal energy, we can find the current in the heater when the unit is operating, the resistance of the heating coil, and the thermal energy.

Formulae:

The rate of the electrical energy transferred, P = iV …(i)

Here, P is the power, i is current, V is the potential difference.

According to Ohm’s law, the potential difference is given by, V = iR …(ii)

Here, R is the resistance

The thermal energy E is generated by the heater, E = Pt …(iii)

Here, t is the time.

Using the given data in equation (i), we can get the value of the current flowing into the heater as follows:

$\begin{array}{l}i=\frac{1250W}{115V}\\ =10.9A\end{array}$

Hence, the value of the current is 10.9 A.

Using the given data in equation (ii), we can get the value of the resistance in the heating coils as follows:

$\begin{array}{l}R=\frac{115V}{10.9A}\\ =10.6\Omega \end{array}$

Hence, the value of the resistance is $10.6\Omega$.

The thermal energy E is generated by the heater in time t = 3600s is given using the data substituted in equation (iii) as follows:

$$\begin{gathered} E=1250W\times 3600s \\ =4.50\times {10}^{6}J \end{gathered}$$

Hence, the amount of produced thermal energy is $4.50\times {10}^{6}J$.