Problem 1 - College Physics

Question

Typical household currents are on the order of a few amperes. If a 1.50 A current flows through the leads of an electrical appliance, (a) how many electrons per second pass through it, (b) how many coulombs pass through it in 5.0 min, and (c) how long does it take for 7.50 \(\mathrm{C}\) of charge to pass through?

Step-by-Step Solution

Answer

(a) \(9.36 \times 10^{18}\) electrons per second, (b) 450 C in 5 min, (c) 5 seconds.

Step 1: Understanding the problem

We need to find the number of electrons and the amount of charge passing through an electrical appliance with a given current. Then, calculate the time needed for a certain charge to pass through. Given current is 1.50 A.

Step 2: Calculate electrons per second (a)

First, we'll use the formula relating current to charge: \( I = \frac{Q}{t} \), where \( I \) is the current in amperes, \( Q \) is the charge in coulombs, and \( t \) is time in seconds.For 1.50 A, \( 1.50 = \frac{Q}{1} \) gives \( Q = 1.50 \times 1 \) = 1.50 C per second.We know \( 1 \) coulomb is approximately \( 6.242 \times 10^{18} \) electrons,so the number of electrons per second is:\( 1.50 \times 6.242 \times 10^{18} \approx 9.36 \times 10^{18} \).

Step 3: Calculate charge in coulombs for 5 min (b)

Convert time from minutes to seconds for accuracy, so 5 min = 300 seconds. Use again \( Q = It \), with \( I = 1.50 \, \text{A} \) and \( t = 300 \, \text{s} \):\( Q = 1.50 \times 300 = 450 \) C.

Step 4: Calculate time for 7.50 C to pass (c)

Use the same relation \( I = \frac{Q}{t} \) and solve for \( t \) when \( Q = 7.50 \) C and \( I = 1.50 \) A:\( t = \frac{Q}{I} = \frac{7.50}{1.50} = 5 \) seconds.

Key Concepts

Amperes

An ampere, often abbreviated as "A," is the unit of electric current in the International System of Units (SI). Imagine it as a measure of how much electricity is flowing through a circuit. If you think of electricity like water flowing through a pipe, then an ampere is like measuring the volume of water passing a point in a given time.
For practical understanding:

• If your current is 1 ampere, it means 1 coulomb of charge is passing through a given point in a circuit every second.
• Ampere's unit is derived from the charge and time, where 1 ampere equals 1 coulomb per second.

This unit is crucial because it helps define how electrical appliances are powered. Devices that require the same current can usually be intermixed without affecting their functionality.

Coulombs

Coulombs are the SI unit of electrical charge. Named after the French physicist Charles-Augustin de Coulomb, it quantifies the amount of electricity or charge.

• One coulomb is equivalent to the charge of approximately 6.242 x 10¹⁸ electrons.
• In simpler terms, it tells us how many electrons (and hence the charge they carry) are present in a system.

Expressing charge in coulombs is pivotal in calculations involving electric currents, as it directly ties to the amount of charge passing through a conductor. When analyzing circuits and doing calculations, understanding the relationship between coulombs and other units like amperes and seconds can provide important insights into how an electrical system functions.

Electrons per second

When we talk about electrons per second, we're discussing the rate at which electrons pass a given point in a conductor. This is directly connected to the current. In fact, current can be thought of as a count of electrons flowing per second.

• It's helpful to know that 1 coulomb equals roughly 6.242 x 10¹⁸ electrons.
• A current of 1 ampere implies 6.242 x 10¹⁸ electrons are passing each second.

Understanding electrons per second helps us visualize not just the amount of charge, but the continuous movement that sustains electrical power. It's like counting cars passing a certain point on a highway within a second, representing the flow and activity in a circuit.

Electrical appliance currents

Electrical appliances are designed to operate with specific currents. Typically, household appliances work with currents on the order of a few amperes. Knowing how much current an appliance uses ensures it operates safely and efficiently.

• Appliances like toasters or lamps usually use something between 1-10 amperes.
• Knowing the current usage helps prevent overloading circuits which can cause interruptions or damage.

Correctly matching appliances to circuit capacities is an important part of home electrical safety. As energy consumption becomes more consequential, being informed about how much current our devices use allows for better energy management and avoids electrical mishaps.