Clay is charging his laptop computer battery, which has an adapter rated at 22 V and 3.25 A. A full chargetakes 40 minutes. What electrical resistance does the adapter have? How much charge does the fully chargedlaptop battery contain? What is the power requirement of the adapter? How much energy is used to re-chargethe battery?
Question
Clay is charging his laptop computer battery, which has an adapter rated at 22 V and 3.25 A. A full chargetakes 40 minutes. What electrical resistance does the adapter have? How much charge does the fully chargedlaptop battery contain? What is the power requirement of the adapter? How much energy is used to re-chargethe battery?
Solution
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To find the electrical resistance of the adapter, we can use Ohm's Law, which states that Voltage (V) = Current (I) x Resistance (R). Rearranging for Resistance gives us R = V/I. Substituting the given values, we get R = 22V / 3.25A = 6.77 ohms.
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To find the charge that the fully charged laptop battery contains, we use the formula Q = It, where Q is the charge, I is the current, and t is the time. The time needs to be in seconds, so 40 minutes is 2400 seconds. Substituting the given values, we get Q = 3.25A * 2400s = 7800 Coulombs.
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The power requirement of the adapter can be found using the formula P = VI, where P is power, V is voltage, and I is current. Substituting the given values, we get P = 22V * 3.25A = 71.5 Watts.
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The energy used to recharge the battery can be found using the formula E = Pt, where E is energy, P is power, and t is time. Again, the time needs to be in seconds, so 40 minutes is 2400 seconds. Substituting the given values, we get E = 71.5W * 2400s = 171,600 Joules.
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