To determine which equation correctly relates charge (Δq), time (t), and current (I), we need to understand the fundamental relationship between these quantities.
1. Current (I): In electrical terms, the current is the rate of flow of electric charge. It can be expressed by the formula:
[tex]\[ I = \frac{\Delta q}{t} \][/tex]
where:
- [tex]\( I \)[/tex] is the current measured in amperes (A),
- [tex]\( \Delta q \)[/tex] is the electric charge measured in coulombs (C),
- [tex]\( t \)[/tex] is the time measured in seconds (s).
2. Analyzing the options:
- Option 1: [tex]\( 1 = \frac{\Delta q}{t} \)[/tex]
This implies that the ratio of charge to time is always 1, which suggests that for any charge and time, their ratio must be constant and always equal to 1. This is not generally true for any charge and any time.
- Option 2: [tex]\( I = \frac{t}{\Delta q} \)[/tex]
This suggests that current is equal to the time divided by the charge, which is incorrect since it inversely relates time and charge to current.
- Option 3: [tex]\( I = \Delta q t \)[/tex]
This implies that current is the product of charge and time, which is incorrect since current is a rate and should involve the division of charge by time, not their multiplication.
- Option 4: [tex]\( I = \Delta q + 1 \)[/tex]
This suggests that current is equal to the charge plus 1, which is not supported by any physical laws relating charge, time, and current.
Thus, considering these options, the correct equation that describes the relationship between charge, time, and current is:
[tex]\[ I = \frac{\Delta q}{t} \][/tex]
Given the answer from our analysis, the correct option number is:
- Option 1: [tex]\( I = \frac{\Delta q}{t} \)[/tex]
Therefore, the choice that correctly describes the relationship between charge (Δq), time (t), and current (I) is:
[tex]\[ 1 = \frac{\Delta q}{t} \][/tex]
