# 19fa-1910-workshop01-battery-sol.pdf - MATH 1910 Workshop...

• Homework Help
• 5

This preview shows page 1 - 2 out of 5 pages.

MATH 1910 Workshop Battery Charging Introduction: Dimensional analysis is one important tool for solving engineering problems. Dimensional analysis is the practice of keeping track of all units in a problem and making sure the results have the expected units, or dimensions. Numbers by themselves are meaningless without the corresponding units: 1 meter = 100 centimeter, but 1 does not equal 100. The number and the unit are inseparable, at least in principle! Writing 1 meter rather than 1 is called “carrying the unit.” As a general rule, units should be carried in all engineering computations and treated as algebraic quantities. It is best to work out the equations in symbolic form, replacing each symbol by its number and unit only at the very end. Dimensional analysis 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 an error. The units we will use in this workshop 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), Volts (the standard unit of potential, 1 V = 1 J / C), and Watts (the standard unit of power, 1 W = 1 J / s). 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 T f = 9 hours if the voltage buildup has the temporal form: V ( t ) = a p t/τ where a = 7 Volt, and where the constant parameter τ = 3 hours.