Problem 14 - Applied Physics

Question

How many amperes will a 60 -W lamp draw on a \(11 \overline{0}-\mathrm{V}\) line?

Step-by-Step Solution

Answer

The lamp draws approximately 0.55 amperes.

Step 1: Understand the Power Formula

To find the current in amperes, we need to use the formula for electrical power: \[ P = V \times I \]where \( P \) is the power in watts, \( V \) is the voltage in volts, and \( I \) is the current in amperes. We are given \( P = 60 \) W and \( V = 110 \) V. We need to solve for \( I \).

Step 2: Rearrange the Power Formula

From the power formula \( P = V \times I \), solve for \( I \) by rearranging the equation:\[ I = \frac{P}{V} \]This formula lets us find the current when the power and voltage are known.

Step 3: Substitute Values into the Formula

Substitute the known values into the rearranged formula:\[ I = \frac{60}{110} \]Perform the division to find \( I \).

Step 4: Calculate the Current

Calculate \( I \) by dividing 60 by 110:\[ I = \frac{60}{110} \approx 0.5454545 \]For practical purposes, we round to two decimal places, resulting in \( I \approx 0.55 \) amperes.

Key Concepts

Power Formula

The power formula is a fundamental principle in electrical engineering that relates power, voltage, and current. The formula is given by \( P = V \times I \). Here, \( P \) stands for electrical power measured in watts, \( V \) represents the voltage in volts, and \( I \) is the current in amperes. This equation is essential for calculating the power used by an electrical device when the voltage and current are known.
This formula shows the direct relationship between these quantities. To find any one of them, you can rearrange the formula as needed. For instance:

• To find power \((P)\), use the formula: \( P = V \times I \).
• To find voltage \((V)\), use: \( V = \frac{P}{I} \).
• To determine current \((I)\), rearrange to: \( I = \frac{P}{V} \).

This flexibility makes the power formula an invaluable tool for solving diverse electrical problems.

Voltage

Voltage is a measure of electrical potential difference between two points in a circuit. It is often likened to the pressure of water flowing through a pipe. Just as higher water pressure means more water can flow through a pipe, higher voltage means more electric charge can flow through a circuit.
In the power formula, voltage \((V)\) is a key component. Knowing the voltage helps in calculating the power or current, given the other variables. Voltage is measured in volts (V), which defines how much potential energy per unit charge is available to move electrons through a conductor.
When you plug a device into an outlet, it "sees" a certain voltage, which determines how it operates. For our example, the voltage of the line is 110 volts, a common household voltage level.

Electrical Power

Electrical power quantifies the rate at which electrical energy is consumed or produced by a device. It is expressed in watts \((W)\). In the context of our exercise, a 60-watt lamp uses its electrical power to produce light.
Power in electrical circuits is crucial as it indicates how much energy is being transformed. For example, in a light bulb, power determines the amount of light and heat emitted. This is why different bulbs with higher wattages will provide more light.
Using the power formula \( P = V \times I \), one can calculate power if the current and voltage are known. If either voltage or current is unknown, rearranging the formula helps uncover the missing variable, aiding in determining how much energy your appliances are consuming.

Ohm's Law

Ohm's Law is another fundamental concept in electricity that relates voltage, current, and resistance. Although different from the power formula, understanding Ohm's Law complements your knowledge of electrical circuits. Ohm's Law is given by \( V = I \times R \), where \( R \) stands for resistance in ohms \((\Omega)\).
This principle helps in determining how much voltage is needed to drive a current through a certain resistance. While it is not directly used in solving our original exercise, it sheds light on the interaction between current and resistance.
For practical use, Ohm's Law can help you:

• Find voltage \((V)\): \( V = I \times R \).
• Determine current \((I)\): \( I = \frac{V}{R} \).
• Calculate resistance \((R)\): \( R = \frac{V}{I} \).

Understanding Ohm's Law alongside the power formula provides a comprehensive view of how electrical circuits operate.