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Which of the following is the correct formula for the amount of charge flowing through a point in a circuit in a given time?
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π represents the amount of charge, πΌ represents the current, and π‘ represents time.
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In this example, weβre looking for the correct formula out of the four choices weβre given, A, B, C, and D, that represents the amount of charge, π, flowing through a point in a circuit over a given time.
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In other words, we want to know mathematically how it is that charge π, current πΌ, and time π‘ are related.
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It will be helpful to us to recall the general definition of just what a current is.
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Current is a measure of the amount of flowing material passing by a point in some amount of time.
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When it comes to electric current, that flowing material is charge.
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We represent that using the letter π.
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And we can represent some amount of time using the letter π‘.
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Since current has to do with the amount of charge passing a point per unit time, we can divide π by π‘, and that will give us the current, which we symbolize with πΌ.
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We now have a mathematical equation for current.
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Letβs see if we find this equation anywhere among our answer options.
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Looking first at answer option A, we see that that claims that current is equal to charge times time.
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But our equation shows that current is equal to charge divided by time.
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This means that option A is not the correct formula.
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All the remaining options after this one have π isolated by itself on one side of the equation.
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In order to see how our equation compares, letβs algebraically rearrange it so that π is on one side by itself.
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To do this, we can take our equation and multiply both sides of it by the time passed π‘.
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When we do this, π‘ on the right-hand side of the equation cancels out since itβs in both numerator and denominator.
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Our equation now reads π, the charge, is equal to πΌ times π‘.
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And we see that, of the three choices B, C, and D, itβs D that matches up with this expression.
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So the correct formula for the amount of charge flowing through a point in a circuit over a given time is π is equal to πΌ times π‘.