To determine the correct equation that relates charge ([tex]\(\Delta q\)[/tex]), time (t), and current (I), let's understand the fundamental relationship between these physical quantities.
The relationship between charge, current, and time is given by the definition of electric current. Electric current ([tex]\(I\)[/tex]) is defined as the rate of flow of electric charge.
The mathematical relationship is expressed as:
[tex]\[
I = \frac{\Delta q}{t}
\][/tex]
Here, [tex]\(I\)[/tex] represents the current, [tex]\(\Delta q\)[/tex] represents the amount of electric charge that passes through a given point, and [tex]\(t\)[/tex] represents the time interval during which the charge flows. This equation indicates that the current is equal to the charge divided by the time.
Given the four options, we can identify the correct one based on our understanding of this relationship:
1. [tex]\(I = \frac{\Delta q}{t}\)[/tex]
2. [tex]\(I = \frac{t}{\Delta q}\)[/tex]
3. [tex]\(I = \Delta q t\)[/tex]
4. [tex]\(t = \Delta q + t\)[/tex]
- Option 1: This equation [tex]\(I = \frac{\Delta q}{t}\)[/tex] directly matches the fundamental definition of current. It correctly relates charge, current, and time.
- Option 2: [tex]\(I = \frac{t}{\Delta q}\)[/tex] does not represent the correct relationship since it implies that the current is equal to the time divided by charge, which is not accurate.
- Option 3: [tex]\(I = \Delta q \cdot t\)[/tex] incorrectly suggests that current is the product of charge and time, which again is not correct.
- Option 4: [tex]\(t = \Delta q + t\)[/tex] is not a valid equation for relating these quantities, as it implies an incorrect arithmetic sum of charge and time.
Therefore, the correct equation that relates charge ([tex]\(\Delta q\)[/tex]), time (t), and current (I) is:
[tex]\[
I = \frac{\Delta q}{t}
\][/tex]
Hence, the correct option is:
[tex]\[
1
\][/tex]
