Problem 3 - Applied Physics

Question

How many amperes will a \(75.0\) -W lamp draw on a \(11 \overline{0}-\mathrm{V}\) line?

Step-by-Step Solution

Answer

The lamp draws approximately 0.6818 amperes.

Step 1: Understand the Formula

To find the current (in amperes) that the lamp draws, we need to use the formula relating power, voltage, and current: \[ P = V imes I \] where \( P \) is the power in watts, \( V \) is the voltage in volts, and \( I \) is the current in amperes.

Step 2: Rearrange the Formula

We need to solve for the current \( I \). Rearrange the formula to isolate \( I \):\[ I = \frac{P}{V} \]

Step 3: Substitute the Values

Now substitute the given values into the equation: \( P = 75.0 \) watts and \( V = 110 \) volts.\[ I = \frac{75.0}{110} \]

Step 4: Calculate the Current

Perform the division to find the current:\[ I = 0.6818 \] amperes (rounded to four decimal places).

Key Concepts

Electrical Power Formula

Electrical power is an essential concept when dealing with electrical circuits. This formula helps us understand the relationship between power (P) in watts, voltage (V) in volts, and current (I) in amperes. The formula is as follows: \[ P = V \times I \].
Power (P) represents the rate at which energy is consumed or generated by a device.
Voltage (V) is the potential difference that drives electric charge through the circuit. Current (I) is the flow of electric charge.

• A higher voltage or current increases power consumption in a circuit.
• Power is crucial to understanding how much energy a device uses over time.

Using the power formula, you can calculate any of these variables if the other two are known, making it extremely useful for solving circuit-related problems.

Current Calculation

Calculating the current in an electrical circuit is a straightforward process once you know the power and voltage.
From the Electrical Power Formula, we can derive the formula for current (I) as follows: \[ I = \frac{P}{V} \].
When performing the calculation, simply plug in the known values of power (P) and voltage (V) into the equation.

• The unit for current is amperes (A).
• Ensure that you use consistent units such as watts for power and volts for voltage.

Current calculation is essential for determining how much electricity is flowing through a device, like a lamp, and gauging if the circuit can handle this load without overheating or causing other issues.

Voltage and Current Relationship

Voltage and current have a direct and crucial relationship in the context of electrical circuits. Ohm's Law and the Electrical Power Formula both illustrate these dynamics.
According to the Electrical Power Formula, current ( I ) is directly proportional to power ( P ) when voltage ( V ) is constant.
This means:

• Increasing voltage will lead to a higher current, assuming that power consumption remains unchanged.
• For any electrical device, balancing voltage and current is vital for optimal operation.

Understanding this relationship helps in designing circuits and selecting appropriate components to ensure they function efficiently and safely. It's this balance that prevents overloads and maintains the stability of electrical systems.