If a 2.5 A current flows through a circuit for 35 minutes, how many coulombs of charge moved through the circuit?

Have you ever wondered what makes the lights in your home turn on, or how your phone charges? At the heart of these processes is an electric current, which is measured in amperes, often shortened to 'amps'. This unit of measurement, symbolized by the letter 'A', tells us the rate at which electric charge is flowing through a conductor, such as a wire.

In simple terms, think of the current as a crowd of people (electric charges) moving through a hallway (the conductor). The larger the crowd that moves through in a given amount of time, the stronger the current is. In the problem given, the 'crowd' is a certain number of electric charges passing through a section of the circuit every second, creating a current of 2.5 amps.

Why is Current Important?

Current is a fundamental concept in electronics and electrical engineering because it directly correlates with the amount of electricity being used or transferred. Understanding current helps in designing safe circuits that can handle the flow without overheating or causing damage.

You've probably heard phrases like 'just a second' or 'give me a minute', but when it comes to calculations involving electric currents, time needs to be precise. It's often necessary to convert time from one unit to another to use certain formulas correctly.

In our exercise, we deal with time conversion by switching from minutes to seconds because our formula requires time in seconds. To convert minutes to seconds, multiply the number of minutes by 60, as there are 60 seconds in one minute. This conversion is not just about following a mathematical procedure; it's about ensuring consistency in units to get accurate and meaningful results in science and engineering calculations.

• 1 minute = 60 seconds
• To convert 35 minutes to seconds: 35 minutes * 60 seconds/minute = 2100 seconds

The conversion allows us to plug the correct time value into the formula, ensuring the charge is calculated accurately.

The coulomb, symbolized by 'C', is the SI unit of electric charge. It's named after Charles-Augustin de Coulomb, an 18th-century physicist who studied electric forces. One coulomb represents the quantity of electricity transported in one second by a current of one ampere.

It's important to grasp how this unit is used to measure the amount of electric charge. When we talk about coulombs in our exercise, we're essentially counting the 'electrical citizens' moving through our 'hallway'. The question we're answering is, how many of these 'citizens' (electric charges) pass a certain point when a known current flows for a given period?

Calculating Charge in Coulombs

To find out, we multiply the current in amperes by the time in seconds (this operation is equivalent to counting all the people passing through the hallway over a certain period). In standard formula form, it looks like this: \(Q = I \times t\), where \(Q\) is the charge in coulombs, \(I\) is the current in amperes, and \(t\) is the time in seconds. In our exercise, we calculated that a current of 2.5 amps flowing for 2100 seconds results in 5250 coulombs of charge passing through the circuit.