Understanding Electric Charge Calculation

This problem requires us to calculate the total electric charge that passes through an electrical machine when a known current flows through it for a specific duration. The fundamental relationship connecting charge, current, and time is crucial here.

Relationship Between Charge, Current, and Time

Electric current ($\text{I}$) is defined as the rate of flow of electric charge ($\text{Q}$) through a conductor over a period of time ($\text{t}$). Mathematically, this relationship is expressed as:

\( \text{I} = \frac{\text{Q}}{\text{t}} \)

From this formula, we can rearrange it to find the total charge ($\text{Q}$) that flows:

\( \text{Q} = \text{I} \times \text{t} \)

Given Information in the Problem

We are provided with the following values:

• Current through the electrical machine ($\text{I}$) = 15 A
• Time the machine runs ($\text{t}$) = 10 minutes

We need to find the total charge ($\text{Q}$) that passes through the machine during this time.

Units and Necessary Conversion

In the formula \( \text{Q} = \text{I} \times \text{t} \), the standard units in the International System of Units (SI) are Amperes (A) for current, seconds (s) for time, and Coulombs (C) for charge. The given current is in Amperes, which is correct. However, the time is given in minutes, so we must convert it to seconds before performing the calculation.

The conversion factor is:

1 minute = 60 seconds

Therefore, 10 minutes is equal to:

\( \text{t} = 10 \text{ minutes} \times \frac{60 \text{ seconds}}{1 \text{ minute}} = 600 \text{ seconds} \)

Calculating the Electric Charge Passed

Now that we have the current in Amperes and the time in seconds, we can use the formula \( \text{Q} = \text{I} \times \text{t} \) to calculate the total charge:

Given:

• $\text{I} = 15$ A
• $\text{t} = 600$ s

Calculation:

\( \text{Q} = 15 \text{ A} \times 600 \text{ s} \)

\( \text{Q} = 9000 \text{ A} \cdot \text{s} \)

Since 1 Ampere is equal to 1 Coulomb per second (1 A = 1 C/s), the unit A⋅s is equivalent to Coulombs (C).

\( \text{Q} = 9000 \text{ C} \)

Thus, the total charge that passes through the electrical machine during 10 minutes is 9000 Coulombs.

Revision Table: Key Concepts

Additional Information: Understanding Units

Let's look a bit deeper into the units involved:

• Coulomb (C): The SI unit of electric charge. One Coulomb is the amount of charge transported by a constant current of one ampere in one second. It is named after French physicist Charles-Augustin de Coulomb.
• Ampere (A): The SI unit of electric current. One Ampere is defined as the flow of one Coulomb of charge per second (1 A = 1 C/s). It is named after French mathematician and physicist André-Marie Ampère.
• Second (s): The SI unit of time.

Understanding these units helps clarify the formula \( \text{Q} = \text{I} \times \text{t} \). If current is in Coulombs per second (C/s) and time is in seconds (s), then their product correctly gives the charge in Coulombs (C): \( \frac{\text{C}}{\text{s}} \times \text{s} = \text{C} \).

This problem demonstrates a direct application of the definition of electric current and highlights the importance of using consistent units (SI units in this case) for calculations in physics.