workshop 2 problem 1

# workshop 2 problem 1 - -1 Problem Battery We will insist on...

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1 Problem. Battery We will insist on the importance of units in engineering applications. In addition to being important for applications in the real world, keeping track of units is a powerful way to check that an answer is at least consistent with the expected outcome. Getting the units right does not guarantee that the answer is right, but getting them wrong is a clear indication of difﬁculty. The units we will use in this problem are Coulombs (the standard unit of charge, denoted C ), Joules (the standard unit of energy, 1 J = 1 kg · m 2 / s 2 ), Amperes (the standard unit of current, 1 A = 1 C / s ), and Volts (the standard unit of potential, 1 V = 1 J / C ). A car battery is charged with a constant current source of I = 20 Amperes. The object is to calculate the amount of energy in Joules stored in the battery after 9 hours if the voltage buildup has the temporal form: V ( t ) = 7 p t/t 0 Volts where the constant parameter t 0 = 3 hours. Figure 1: Calculation of the energy stored in a typical car battery after it is charged by a

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workshop 2 problem 1 - -1 Problem Battery We will insist on...

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