Problem 13 - Applied Physics

Question

Electric characteristics of all consumer electric devices must be shown on an attached plate. What is the resistance of an iron that discloses \(6.40 \mathrm{~A}\) of current used on a \(12 \overline{0}\) - \(\mathrm{V}\) line?

Step-by-Step Solution

Answer

The resistance is 18.75 ohms.

Step 1: Identify the known values

From the problem statement, we know the current \( I = 6.40 \!\text{ A} \) and the voltage \( V = 120 \!\text{ V} \).

Step 2: Recall Ohm's Law

Ohm's Law is given by the formula \( V = IR \), where \( V \) is voltage, \( I \) is current, and \( R \) is resistance.

Step 3: Rearrange Ohm's Law to find Resistance

We need to find the resistance \( R \). Rearrange the formula to solve for \( R \): \[ R = \frac{V}{I} \]

Step 4: Substitute known values into the formula

Plug in the known values into the equation: \[ R = \frac{120 \!\text{ V}}{6.40 \!\text{ A}} \]

Step 5: Calculate the resistance

Perform the division to find \( R \): \[ R = 18.75 \!\text{ ohms} \]

Key Concepts

Electric resistance

Electric resistance is a measure of how much an electrical device or material opposes the flow of electric current. Think of it like a narrow pipe that resists the flow of water; the narrower the pipe, the harder it is for water to flow through. Similarly, higher resistance means it's harder for electric current to pass through a material or device.

The unit of electric resistance is the Ohm, symbolized by \( \Omega \). Resistance is calculated by dividing voltage (V) by current (I), which is well-represented by the formula \( R = \frac{V}{I} \). In our exercise's context, the iron's resistance tells us how much it opposes the electric current flowing through it when connected to a 120 V line with a 6.40 A current. An intermediate resistance can help prevent excessive current that might damage the device or cause overheating.

Current and Voltage

To understand electric resistance better, it's crucial to grasp the concepts of current and voltage. Electric current refers to the flow of electric charge through a conductor, such as a wire. It is measured in Amperes (A). In simple terms, current is like the flow of water through a pipe. Voltage, on the other hand, is the force that pushes the electric current through the conductor. It is the potential difference between two points and is measured in Volts (V).

When a voltage is applied across a conductor, it creates an electric field that causes charges to flow, thereby creating a current. The relationship between these quantities is captured by Ohm's Law, \( V = IR \), where \( V \) is voltage, \( I \) is the current, and \( R \) is the resistance. The exercise demonstrates how a 120 V line and 6.40 A current interact to produce resistance, illustrating Ohm's Law in action. Understanding this relationship helps you see how devices consume energy.

Consumer electric devices

Consumer electric devices are all around us, from refrigerators to smartphones, and each has specified electrical requirements to function properly. These specifications, often displayed on attached plates or labels, inform users about the device's voltage and current specifications, and sometimes its power and electrical resistance.

Knowing a device's electric characteristics helps ensure you connect it to suitable power sources, preventing damage. If a device is designed for a certain voltage and current, plugging it into a different power level could result in suboptimal performance or even harm. In our exercise, the iron works optimally when it draws 6.40 A from a 120 V line, showing the importance of these specifications in daily life.

• Ensures safety by preventing electrical overload.
• Helps achieve optimal device performance.
• Guides users to compatible power sources.