Problem 19 - Applied Physics

Question

At what rate does a light bulb convert electric energy to light if it draws \(0.500 \mathrm{~A}\) of current on a \(12 \overline{0}\) -V outlet?

Step-by-Step Solution

Answer

The light bulb converts electric energy to light at 60 watts.

Step 1: Identify the Known Values

We are given the current (\(I\)) as \(0.500 \mathrm{~A}\) and the voltage (\(V\)) as \(120 \mathrm{~V}\). We need to find the power (\(P\)), which indicates the rate at which electric energy is converted to light.

Step 2: Use the Power Formula

The formula to calculate power using voltage and current is:\[ P = V \times I \]where \(P\) is power in watts, \(V\) is voltage in volts, and \(I\) is current in amperes.

Step 3: Insert Values and Calculate

Substitute the known values into the formula:\[ P = 120 \mathrm{~V} \times 0.500 \mathrm{~A} \]Now, calculate \(P\):\[ P = 60 \mathrm{~W} \]So, the light bulb converts electric energy to light at a rate of 60 watts.

Key Concepts

Current and Voltage Relationship

In any electrical circuit, there is a fundamental relationship between current (I), voltage (V), and resistance (R). This relationship is often described by Ohm's Law. Ohm’s Law states that voltage is the product of the current flowing through a conductor and the resistance of the conductor to flow of electricity. Mathematically, it is expressed as:\[ V = I imes R \]Where:

• \( V \) is the voltage across the circuit in volts.
• \( I \) is the current through the circuit in amperes.
• \( R \) is the resistance in ohms.

This relationship highlights how changes in voltage or resistance affect the current flow. If resistance remains constant, an increase in voltage leads to a proportional increase in current.
On the contrary, increasing the resistance while maintaining a constant voltage will reduce the current. Understanding this relationship is crucial for solving many electrical engineering problems and is key to designing efficient electrical circuits.

Energy Conversion

Energy conversion in electrical devices is a vital concept in understanding how devices like light bulbs work. Essentially, electrical energy is converted into various forms depending on the device. In the case of a light bulb:

• Electrical energy is converted into light energy, allowing the bulb to illuminate.
• It is also partly converted into heat, which is often why bulbs get warm.

The rate at which this conversion happens is described by the power formula:\[ P = V imes I \]Where \( P \) is the power measured in watts. This formula calculates how much electrical power is used to perform work—in this case, producing light. For instance, if we know a bulb uses 60 watts, it means it's converting 60 joules of electrical energy into light and heat every second.
This conversion process helps us design and use electrical devices effectively, ensuring we meet energy requirements for practical applications.

Light Bulb Efficiency

Efficiency of a light bulb refers to how well it converts electrical energy to light compared to other forms of energy like heat. It is an important metric as it indicates how much light will be produced for a given amount of electrical energy:Efficiency can be represented by the formula:\[ \text{Efficiency} = \frac{\text{Useful energy output}}{\text{Total energy input}} \times 100\%\]In this context:

• The useful energy output is the light energy produced by the bulb.
• The total energy input is the electrical energy the bulb consumes.

For example, if a light bulb converts 60 watts of electrical power but only 30 watts is useful light, its efficiency would be 50%.
Improving this efficiency means producing more light and less heat, which can be achieved by using technologies like LED bulbs that are designed to have higher efficiency levels. Understanding light bulb efficiency helps consumers make informed choices about energy use and helps manufacturers to innovate better products.