A \(35-\Omega\) electric stove burner consumes \(1.5 \mathrm{kW}\) of power. At what voltage does it operate?

Understanding electric power is fundamental when learning about how various appliances consume energy. Electric power describes the rate at which electrical energy is transferred by an electric circuit. The standard unit for power is the watt (W). When you use an electrical device, the power it uses is converted into work or heat. For instance, a stove burner transforms electrical power into heat used for cooking.

The power of a device can be calculated by multiplying the voltage (V) across the device by the current (I) flowing through it, which is expressed in the formula: \(P = VI\). However, when the resistance (R) is known instead of the current, the formula can be modified to \(P = V^2 / R\), which demonstrates how power relates to voltage and resistance. This formula is particularly handy when only the power consumption and resistance are available, as seen in the exercise where an electric stove burner’s power consumption helps calculate its operating voltage.

The concept of electric resistance is critical for understanding how the flow of electric current is impeded within a conductor. Resistance, measured in ohms (Ω), is a material's tendency to resist the flow of charge. This property is an inherent characteristic of the material and geometrical attributes of the conductor.

An analogy often used for resistance is water flowing through a pipe; just as a narrower pipe restricts water flow, a material with high resistance restricts the flow of electric charge. In our stove burner example, the resistance is provided as \(35-Ω\), which tells us how much the burner impedes the electric current. This value is essential when coupled with the known power consumption to calculate the voltage required for the burner to operate. Knowing resistance can also help in determining the safety and efficiency of electrical devices since materials with high resistance can produce more heat, which needs to be managed for safe operation.

Voltage calculation is an essential skill in electrical engineering that helps you determine the potential difference required to power an appliance. Voltage, which is measured in volts (V), refers to the potential difference between two points in a circuit and is a driving force that pushes electric charges to move through a conductor.

In the exercise, we're required to find the voltage, given the electric power consumption and the resistance of the stove burner. By rearranging the formula \(P = V^2 / R\) to solve for 'V', which stands for voltage, we get \(V = \sqrt{ P \times R }\). Following the steps provided, we insert the known values and simplify to compute the voltage. This approach demonstrates how to deduce the voltage needed for an appliance when you know how much power it consumes, and its resistance.