Problem 1 - Applied Physics

Question

A heater draws \(8.70 \mathrm{~A}\) on a \(11 \overline{0}-\mathrm{V}\) line. What is its wattage rating?

Step-by-Step Solution

Answer

The wattage rating of the heater is 957 watts.

Step 1: Identify the Formula

To determine the wattage rating, we need to use the formula for electrical power: Power (P) is calculated as the product of current (I) and voltage (V). The formula is given by: \[ P = I \times V \] where \( I \) is current in amperes and \( V \) is voltage in volts.

Step 2: Plug in the Given Values

Based on the problem, the current \( I \) is \(8.70 \, \text{A} \) and the voltage \( V \) is \( 110 \, \text{V} \). Substitute these values into the power formula: \[ P = 8.70 \, \text{A} \times 110 \, \text{V} \]

Step 3: Calculate the Power

Perform the multiplication to find the power: \[ P = 8.70 \times 110 = 957 \, \text{W} \]. Thus, the wattage rating of the heater is 957 watts.

Key Concepts

Ohm's Law

Ohm's Law is an essential principle in the study of electricity. It helps us understand how current, voltage, and resistance relate to each other. In simple terms, Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. The law is mathematically expressed as:\[ I = \frac{V}{R} \]where:- \( I \) is the current in amperes (A)- \( V \) is the voltage in volts (V)- \( R \) is the resistance in ohms (\(\Omega\))This fundamental law is crucial because it allows us to calculate any one of these three variables if the other two are known. In practical terms, understanding Ohm's Law helps ensure that electrical devices operate safely by not exceeding the rated current of the components involved.

Current and Voltage

To understand electricity, it's important to know about current and voltage, two key concepts. Current refers to the flow of electric charge and is measured in amperes (A). Think of it like the flow of water in a pipe. Just as water needs a pressure difference to flow, electrical current requires a potential difference to move through a circuit. Voltage, on the other hand, is the force or "pressure" that pushes the current through a conductor. It is measured in volts (V). Together, current and voltage determine how much power an electrical device can consume. For example, in the given exercise, a heater with a current of 8.70 A and a voltage of 110 V draws an amount of power that can be calculated using these values.

Wattage Rating

The wattage rating of an electrical device is a measure of its power consumption. It represents how much energy is used by the device over time and is expressed in watts (W). The formula to calculate power, or wattage, is given by:\[ P = I \times V \]where:- \( P \) is the power in watts- \( I \) is the current in amperes- \( V \) is the voltage in voltsThis equation tells us that power is the product of current and voltage. For instance, in the original exercise, by applying the given current and voltage values into the formula, you arrive at a power rating of 957 watts for the heater. A higher wattage rating indicates that a device uses more electricity to operate, often leading to a more powerful output, but also resulting in a greater energy cost. Therefore, understanding wattage rating is crucial for both energy efficiency and managing power consumption.