Understanding Electric Current, Charge, and Time

The question asks us to identify the correct relationship between net charge (Q), time (t), and electric current (I).

Electric current is a fundamental concept in physics, representing the flow of electric charge. It is defined as the rate at which electric charge passes through a specific point or region per unit of time.

Let's define the terms:

• Net Charge (Q): The total amount of electric charge that flows. The unit of charge is the Coulomb (C).
• Time (t): The duration over which the charge flows. The unit of time is the second (s).
• Electric Current (I): The rate of flow of charge. The unit of electric current is the Ampere (A).

The definition of electric current directly gives us the relationship between these three quantities. If a net charge \(Q\) passes through a point in time \(t\), the electric current \(I\) is given by the formula:

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

This formula states that the electric current is equal to the amount of charge flowing divided by the time taken for that charge to flow. This equation is crucial for understanding basic circuits and charge movement.

Analyzing the Given Options

Let's examine each of the provided options and compare them with the standard definition of electric current \(I = \frac{Q}{t}\).

Option 1: \(t = Q \times I\)

To check if this is correct, we can rearrange it to solve for I:

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

This equation suggests that current is proportional to time and inversely proportional to charge, which contradicts the definition where current is proportional to charge and inversely proportional to time.

Analysis: Incorrect.

Option 2: \(I = \frac{Q}{t}\)

This equation directly matches the definition of electric current as the rate of flow of charge (charge divided by time).

Analysis: Correct.

Option 3: \(Q = \frac{I}{t}\)

To check this option, let's rearrange it to solve for I:

\(I = Q \times t\)

This equation suggests that current is proportional to both charge and time, which is incorrect based on the definition. Current is the rate of flow, meaning it depends on the amount of charge *per unit time*, not the product of charge and time.

Analysis: Incorrect.

Option 4: \(I = Q \times t\)

This is the same relationship derived from Option 3. As explained above, this is incorrect. Current is defined by division of charge by time, not multiplication.

Analysis: Incorrect.

Based on the definition of electric current, the correct equation relating net charge (Q), time (t), and electric current (I) is \(I = \frac{Q}{t}\).

Summary of Options

The only equation that correctly defines electric current based on the flow of net charge over time is \(I = \frac{Q}{t}\).

Revision Table: Electric Current Basics

From the relationship \(I = \frac{Q}{t}\), we can see that 1 Ampere is equal to the flow of 1 Coulomb of charge per 1 second. \(1\text{ A} = 1\text{ C/s}\).

Additional Information: Relating Charge, Current, and Time

The equation \(I = \frac{Q}{t}\) can be rearranged to find other quantities if two are known:

• To find the net charge (Q) that flows in a given time (t) at a constant current (I): \(Q = I \times t\).
• To find the time (t) it takes for a certain charge (Q) to flow at a constant current (I): \(t = \frac{Q}{I}\).

It's important to remember that this basic formula for current applies when the current is constant (DC - Direct Current). If the current varies with time (AC - Alternating Current), the definition is expressed using calculus as \(I = \frac{dQ}{dt}\), where \(dQ\) is a small amount of charge flowing in a small time interval \(dt\). The net charge flowing over a specific time period would then be found by integrating the current with respect to time.

In the context of this multiple-choice question and its options, the formula \(I = \frac{Q}{t}\) represents the average or constant electric current.