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The diagram shows an electric circuit containing a cell and a bulb.
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The amount of charge flowing past point ๐ in one second is 12 coulombs.
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If the amount of charge flowing past point ๐ in one second were to double, by what factor would the current in the circuit change?
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Okay, since weโre talking about current here, letโs begin by recalling what it is and how itโs measured.
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Electric current is the flow of electric charge.
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And in a circuit, current measures how much charge flows past a point in the circuit in one second.
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Now, in this circuit, weโve been told that a charge of 12 coulombs flows past point ๐ every second.
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But what we want to focus on is this.
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If we were to double the amount of charge that passes by point ๐ in one second, how would the current in the circuit be affected?
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Specifically, by what factor would the value of current change?
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Keep in mind that when we say factor here, we simply mean a number that multiplies some other number.
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For example, if we double the charge passing point ๐, then weโre multiplying the charge passing point ๐ by a factor of two.
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However, without even doing any math, we might notice that the answer to this question can be found in the very definition of electric current.
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Current is how much charge flows past a point in one second.
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So, if we double how much charge flows past a point in one second, which is the same thing as current, it makes sense that weโre doubling the current itself.
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This is good evidence that the answer is two.
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Still, to be extra confident in our answer, we can think about the mathematical relationship between charge and current.
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Letโs recall the formula for electric current: ๐ผ equals ๐ divided by ๐ก, where ๐ผ is the current, ๐ represents charge, and ๐ก is time.
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In this question, weโre thinking about multiplying the charge ๐ by two and wondering how this would affect current ๐ผ.
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Notice though that the value for time ๐ก is staying the same; itโs not changing.
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In both cases, with and without the double charge, weโre only measuring how much charge flows past point ๐ in one second.
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So we have a fraction.
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If we double the numerator and just leave the denominator as it is, how is the total value of the fraction affected?
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It doubles.
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Thus, if we double the amount of charge passing through the circuit per second, we double the amount of current in the circuit.
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All we must do now is remember that to double the current means to multiply it by a factor of two.
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So, just using our understanding of electric current, weโve determined that in the circuit if the amount of charge flowing past point ๐ in one second were to double, the current in the circuit would change by a factor of two.