91Ó°ÊÓ

In this problem, we need to determine the current flowing through a radiant heater. The key formula to use is the power formula: \[ P = IV \]Here, \(P\) is the power in watts (W), \(I\) is the current in amperes (A), and \(V\) is the voltage in volts (V). We are given that the heater's power is \(1250 \, \text{W}\) and the voltage is \(115 \, \text{V}\). To find the current, we rearrange the formula:\[ I = \frac{P}{V} \]By substituting the given values:\[ I = \frac{1250}{115} \ I \approx 10.87 \, \text{A} \]So, the current flowing through the heater is approximately \(10.87 \, \text{A}\).

Ohm's Law is fundamental for understanding the relationship between voltage, current, and resistance. The formula is:\[ V = IR \]Where \(V\) is the voltage, \(I\) is the current, and \(R\) is the resistance. We already know \(V = 115 \, \text{V}\) and \(I \approx 10.87 \, \text{A}\). To solve for resistance, we rearrange the formula:\[ R = \frac{V}{I} \]Substituting the known values:\[ R = \frac{115}{10.87} \approx 10.58 \, \text{Ω} \]Thus, the resistance of the heating coil is about \(10.58 \, \text{Ω}\). Simple applications of Ohm's Law let us determine important parameters in an electrical circuit from only a couple of known values.

The last part of this problem involves calculating the thermal energy produced by the heater in one hour. Thermal energy produced can be found using the formula:\[ E = Pt \]Where \(E\) is the energy in joules (J), \(P\) is the power in watts (W), and \(t\) is the time in seconds (s). We are given a power of \(1250 \, \text{W}\) and a time of one hour, which we need to convert to seconds:\[ 1 \, \text{hour} = 3600 \, \text{seconds} \]Now, substituting the values into the formula:\[ E = 1250 \times 3600 = 4500000 \, \text{J} \]The heater produces \(4500000 \, \text{J}\) (or \(4.5 \, \text{MJ}\)) of thermal energy in one hour. This example shows how power and time together determine the thermal energy output of an electrical device.