Problem 5 - Applied Physics

Question

Find the resistance that draws \(0.750 \mathrm{~A}\) on \(115 \mathrm{~V}\).

Step-by-Step Solution

Answer

The resistance is approximately 153.33 Ohms.

Step 1: Identify the Given Values

First, note the values provided in the problem. We have the current \( I = 0.750 \text{ A} \), and the voltage \( V = 115 \text{ V} \). We are asked to find the resistance \( R \).

Step 2: Recall Ohm's Law

Ohm's Law relates voltage, current, and resistance through the formula: \( V = I \times R \). To find the resistance, we can rearrange this formula to \( R = \frac{V}{I} \).

Step 3: Substitute the Given Values into the Formula

Use the values for voltage and current to substitute into the resistance formula: \[ R = \frac{115}{0.750} \]

Step 4: Calculate the Resistance

Perform the division to find the resistance: \[ R = \frac{115}{0.750} \approx 153.33 \text{ Ohms} \]

Step 5: Conclusion

Thus, the resistance of the component that draws \(0.750 \text{ A}\) on \(115 \text{ V}\) is approximately \(153.33 \text{ Ohms} \).

Key Concepts

Resistance Calculation

When it comes to understanding the concept of resistance in a circuit, we rely on the foundational principle known as Ohm's Law. This law helps us determine how much a material resists the flow of electric current.To calculate resistance, the formula we use is:\[ R = \frac{V}{I} \]This shows that resistance \( R \) is calculated by dividing the voltage \( V \) by the current \( I \). This relationship is crucial because it allows us to predict how a change in voltage or current will affect resistance.

Key considerations in resistance calculation:

• Units: Resistance is measured in Ohms (\( \Omega \)).
• Impact on circuits: Higher resistance means less current flows through a circuit for a given voltage.
• Practical use: Knowing resistance helps in designing circuits and choosing appropriate materials.

Electrical Current

Electrical current represents the flow of electric charge through a conductor, typically measured in Amperes (A). Think of current as a stream of water flowing through a pipe. Just as water moves through the pipe, electric charges move through a conductor. There are a few fundamental aspects of electrical current:

• Direction: By convention, current flows from the positive to the negative terminal of a power source.
• Magnitude: The amount of current flowing is affected by both the voltage and the resistance in the circuit.
• DC vs AC: Direct Current (DC) flows steadily in one direction, whereas Alternating Current (AC) changes direction periodically.

Understanding current is essential for analyzing how much energy is transferred in an electrical circuit. More current typically means more power being used or transferred, influencing the design and safety of electrical systems.

Voltage

Voltage can be thought of as the "pressure" that pushes electric charges through a conductor. It is analogous to how water pressure pushes water through pipes. Measured in Volts (V), voltage is a key factor in determining how much current flows in a circuit. Here's what to know about voltage:

• Energy source: Voltage originates from energy sources like batteries or power supplies.
• Electric potential difference: It denotes the difference in electric potential energy between two points.
• Relation to work: Higher voltage implies more work can be done by current flowing through the circuit.

Voltage is crucial because it determines how much current can flow through a circuit for a given resistance. Understanding voltage helps to correctly design circuits and ensure devices operate safely and efficiently.