Problem 16 - Applied Physics

Question

What is the current used by a microwave oven with resistance \(20.0 \Omega\) in a 120 - \(\mathrm{V}\) system?

Step-by-Step Solution

Answer

The current used by the microwave oven is 6 A.

Step 1: Understand the Given Data

We are given the resistance of the microwave oven as \( R = 20.0 \, \Omega \) and the voltage of the electrical system as \( V = 120 \, V \). We need to find the current used by the microwave oven.

Step 2: Apply Ohm's Law

Ohm's Law relates voltage (\( V \)), current (\( I \)), and resistance (\( R \)) in the formula: \( V = IR \). We need to solve for current \( I \), so we rearrange the formula: \( I = \frac{V}{R} \).

Step 3: Substitute Known Values

Substitute the known values of voltage and resistance into the formula: \( I = \frac{120 \, V}{20.0 \, \Omega} \).

Step 4: Calculate the Current

Perform the division to find the current: \( I = \frac{120}{20} = 6 \, \text{A} \).

Key Concepts

Electric Current Calculation

Electric current is a fundamental concept in electrical engineering and physics. It refers to the flow of electric charge in a circuit. This flow is often caused by electrons moving through a conductor, such as a wire. In practical terms, electric current is measured in amperes (A), where one ampere equals the flow of one coulomb of charge per second.

To determine the electric current in a device or circuit, you can use Ohm's Law, which provides a clear relationship between voltage, current, and resistance. Ohm's Law is expressed by the equation: \[I = \frac{V}{R}\]where \( I \) is the current in amperes, \( V \) is the voltage in volts, and \( R \) is the resistance in ohms. This formula allows us to calculate the current used by any electrical component if the voltage across it and its resistance are known.

For example, if a microwave oven has a resistance of 20.0 ohms and is operating on a 120-volt system, the current can be calculated by substituting these values into the formula:

• Voltage \( V = 120 \, V \)
• Resistance \( R = 20.0 \, \Omega \)
• Current \( I = \frac{120}{20.0} = 6 \, A \)

Thus, 6 amperes of current are used by the microwave oven.

Resistance in Circuits

Resistance is a measure of how much a component or material opposes the flow of electric current. It occurs because electrons collide with atoms and molecules in the conducting material, which slows them down. The more collisions, the higher the resistance.

Resistance is measured in ohms (\( \Omega \)), named after Georg Simon Ohm, a German physicist who studied electrical currents. Resistance depends on several factors including:

• Material: Materials like copper and aluminum have low resistance compared to insulators like rubber or wood.
• Length: The longer the conductor, the higher its resistance.
• Thickness: Thicker conductors have lower resistance than thinner ones.
• Temperature: As temperature increases, so does resistance in most conductive materials.

Understanding resistance is crucial for designing circuits, as it helps determine how much current will flow at a given voltage. It also aids in selecting the appropriate materials to minimize energy loss and overheating in electrical devices.

Voltage and Resistance Relationship

Voltage, often referred to as electric potential difference, is the force that pushes electric charge through a circuit. It is measured in volts (V) and represents the energy per unit charge.

There is a direct relationship between voltage, resistance, and current in a circuit as described by Ohm's Law. When voltage increases, with resistance remaining constant, the current also increases, which means more electric charge flows through the circuit. Conversely, if resistance increases while voltage is constant, the current decreases.

This relationship is crucial in electrical engineering and design, as it allows engineers to control how much current flows through circuit components by adjusting resistance and voltage. For instance, using a resistor with higher resistance can decrease current flow, helping to prevent overheating or damage to sensitive components. Conversely, reducing resistance or increasing voltage can increase current flow, which can be useful in applications requiring high power output. Any variation in resistance or voltage greatly influences the behavior and efficiency of electronic devices.