Problem 3 - Applied Physics

Question

An electric heater draws a maximum of \(14.0 \mathrm{~A}\). If its resistance is \(15.7 \Omega\), on what voltage is it operating?

Step-by-Step Solution

Answer

The heater operates at 219.8 V.

Step 1: Identify Known Values

We are given two key quantities: the current drawn by the heater, which is \(I = 14.0 \text{ A}\), and its resistance, \(R = 15.7 \Omega\).

Step 2: Use Ohm's Law

The relationship between voltage (\(V\)), current (\(I\)), and resistance (\(R\)) is given by Ohm's Law: \( V = I \times R \). We will use this formula to find the voltage.

Step 3: Calculate Voltage

Substitute the known values into Ohm's Law: \( V = 14.0 \text{ A} \times 15.7 \Omega \).

Step 4: Perform the Multiplication

Calculate the voltage by performing the multiplication: \( V = 14.0 \times 15.7 = 219.8 \text{ V} \).

Key Concepts

Electric Current

Electric current is essentially the flow of electric charge through a conductor, such as a wire. Imagine it as water flowing through a pipe. The amount of water that flows through the pipe in a certain amount of time is comparable to the electric current. It is measured in amperes (A), often simply called "amps.”

Several factors can influence the electric current:

• Voltage: The higher the voltage, the greater the force pushing the electrons through the conductor.
• Resistance: Resistance hinders electron flow, reducing the current for a given voltage.
• Conductor material: Certain materials allow electrons to flow more easily than others.

For the electric heater in the exercise, the electric current is given as 14.0 A. This tells us the rate at which charge is flowing through the circuit.

Resistance

Resistance is the opposition to the flow of electric current in a material. Imagine trying to walk through a crowd. The more crowded it is, the harder it is to move. That is similar to resistance in an electric circuit.

Resistance is measured in ohms (Ω). It depends on several factors such as:

• Material: Conductors like copper have low resistance, while insulators like rubber have high resistance.
• Length: Longer conductors have more resistance as electrons have a longer path.
• Width: Wider conductors possess less resistance because electrons have more space to pass through.

In our heater example, the resistance of the device is 15.7 Ω. This resistance, combined with the current, determines the voltage needed to operate.

Voltage Calculation

Voltage, often thought of as the electric "pressure" that pushes current through a circuit, needs to be calculated using Ohm's Law in this exercise.

Ohm's Law is a fundamental principle used to calculate the relationship between voltage (V), current (I), and resistance (R). The formula is: \[V = I \times R\]Here, the voltage is the product of the current and the resistance. This tells us how much "force" is needed to get the electrons moving at the current rate through the resistor's opposition.

For the heater:

• Current (I) = 14.0 A
• Resistance (R) = 15.7 Ω

To find the voltage:\[V = 14.0 \times 15.7 = 219.8 \text{ V}\]Thus, the heater needs a voltage of approximately 219.8 volts to operate efficiently. This calculation is crucial in ensuring that the device functions correctly without damage.