Problem 14 - Applied Physics

Question

What is the effective resistance of a television that draws \(2.50 \mathrm{~A}\) on a \(115-\mathrm{V}\) line?

Step-by-Step Solution

Answer

The effective resistance is 46 ohms.

Step 1: Understanding the Known Values

We are given that the television draws a current of \( I = 2.50 \, \text{A} \) and it operates on a voltage of \( V = 115 \, \text{V} \). These are the values we will use in our calculations.

Step 2: Using Ohm's Law

Ohm's Law is given by the formula \( V = I \cdot R \), where \( V \) is the voltage, \( I \) is the current, and \( R \) is the resistance. We are trying to find \( R \).

Step 3: Rearranging Ohm's Law to Solve for Resistance

Rearrange the formula \( V = I \cdot R \) to solve for \( R \). This gives us:\[ R = \frac{V}{I} \]

Step 4: Substituting the Known Values

Substitute the known values into the formula: \( V = 115 \, \text{V} \) and \( I = 2.50 \, \text{A} \). Thus,\[ R = \frac{115}{2.50} \]

Step 5: Calculating the Resistance

Perform the division to find the resistance:\[ R = \frac{115}{2.50} = 46 \text{ ohms} \]

Key Concepts

Electrical Resistance

Electrical resistance is a measure of how much a material opposes the flow of electric current. In essence, it defines how easily charges can move through a material. An easy way to think of resistance is like a traffic blockage that slows down the flow of cars, except in this case, it's electrons flowing through a conductor.
Understanding resistance is crucial because it affects how much current can flow for a given voltage. Materials like copper and silver have low resistance, allowing electricity to flow easily, whereas materials like rubber have high resistance and do not easily allow electricity to pass through.
In practical terms, when dealing with electronics like a television, devices have a certain resistance that determines how much current flows when voltage is applied. Resistance is measured in units called ohms, symbolized by the Greek letter Ω. Knowing the resistance of a device helps ensure that it operates safely and efficiently.

Current Calculation

Current is the rate at which electric charge flows past a point in the circuit; you can think of it as the flow of water through a hose. It's measured in amperes, often shortened to amps (A). Calculating current involves understanding the relationship between voltage, resistance, and current itself.
Using Ohm's Law, represented by the formula \( V = I \cdot R \), we can rearrange it to solve for current if needed. This would be \( I = \frac{V}{R} \). Here, voltage \( V \) is the electric potential difference, and resistance \( R \) is the opposition to flow.
For example, if you know the resistance of a television and the voltage it operates at, you can calculate the current flowing through it using this rearranged formula. This calculation is essential in ensuring that electrical devices do not overheat and are not damaged due to excessive current.

Voltage

Voltage, often referred to as electric potential difference, is the force that pushes electric charges through a conductor. It's like the pressure in a water tank that pushes water out through a pipe. Voltage is essential in determining how much current flows in a circuit and is measured in volts (V).
In circuits, voltage can be provided by batteries or power outlets, like the 115V supplied to a television in our exercise. Higher voltage means more potential for electrical flow, but it also requires careful management to ensure that the circuit elements, such as resistors, are capable of handling it.
Understanding voltage is crucial for the safe and efficient design of electronic devices. It determines how much work can be done by the electrical system, analogous to how much water pressure can turn a water wheel.

Applied Physics

Applied physics utilizes fundamental physics principles to solve practical problems, often leading to new technologies or improving existing ones. Understanding basic concepts like resistance, current, and voltage in electrical systems exemplifies applied physics in electronics.
Applying these principles, engineers and physicists can design circuits that efficiently use power sources, like determining the right resistance for specific components to ensure optimal operation. By knowing the resistance and voltage, one employs applied physics to predict the current that flows, ensuring devices like televisions function correctly without risk of damage.
Thus, applied physics plays a pivotal role in everyday technology. It translates theoretical physics into practical applications, allowing continued innovation and development in electronics and other technological fields.