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A rechargeable battery is left to charge for a period of time.

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It is charged with a current of 10 milliamperes.

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After it has finished, the battery has gained 180 coulombs of charge.

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For how many hours was the battery left to charge?

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In this question, we want to find the number of hours the battery was left to charge for, if it gained 180 coulombs of charge from a current of 10 milliamperes.

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Let’s begin by recalling the definition of electric current.

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Current is the flow of electric charge.

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The current through a point can be expressed by the equation 𝐼 equals 𝑄 divided by 𝑡, where 𝐼 is the current, 𝑄 is the total charge moving past a point, and 𝑡 is the time taken for that amount of charge to move.

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To find the amount of time needed to charge the battery, we need to rearrange this equation to make the time 𝑡 the subject.

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We can do this by multiplying both sides of the equation by 𝑡 and dividing both sides by 𝐼.

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This leaves us with the equation 𝑡 equals 𝑄 divided by 𝐼.

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We are told in the question that the battery has gained 180 coulombs of charge, so we have 𝑄 is equal to 180 coulombs.

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We are also told that the battery is charged with a current of 10 milliamperes, so 𝐼 is 10 milliamperes.

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Notice that there’s this unit prefix, lowercase m or milli-, in the value of the current, so we need to convert this into SI units before we can substitute this value into our equation.

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We can recall that for every one ampere, there are 1000 milliamperes.

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That is, one ampere is equal to 1000 milliamperes.

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So, this means that 10 milliamperes is equal to 10 amperes divided by 1000.

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This is equal to 0.01 amperes.

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We can now substitute these values for the charge and the current into our equation to find that the time the battery was left to charge.

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This time is equal to 180 coulombs divided by 0.01 amperes.

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Completing this calculation, we find that the time is equal to 18000 seconds.

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Now, we note that the question is asking us for the number of hours that the battery was left to charge.

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So we need to convert our answer of 18000 seconds into hours.

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There are 60 seconds in one minute, so we can divide 18000 seconds by 60 to find that the time is equal to 300 minutes.

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There are 60 minutes in one hour, so we can divide 300 minutes by 60 to find that the time is equal to five hours.

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And so we have arrived at our final answer.

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The battery was left to charge for five hours.