Derive the equivalent circuit for a series connection of ideal capacitors. Assume that each capacitor has its own initial voltage. Denote these initial voltages as v1(t0), v2(t0), and so on. (Hint: Sum the voltages across the string of capacitors, recognizing that the series connection forces the current in each capacitor to be the same.)

3 industries that often need the skills of mechanical engineers are:

Automotive industry Construction industry Aerospace industry

The key skills mechanical engineers bring to these industries are effective technical skills, the ability to work under pressure, problem-solving skills, creativity and teamwork.

Explanation:

Automotive industry: The skills mechanical engineers bring to automotive industry include designing new cars for development, conducting laboratory testing for performance safety, and troubleshooting design or manufacturing issues with recalled vehicles. Automotive engineers have:

good mathematical skills, for instance in calculating the stresses power trains and other parts have to withstand;  understanding and application of principles of physics and chemistry to properly design engines, electrical systems and other car components;  good computer skills, because 21st century engineers rely on computer-assisted design software; knowledge of ergonomics, which is applied in the process of designing a car so that the driver and passengers have a comfortable and functional environment, is another skill mechanical; engineers need.

Construction industry: Mechanical engineers are responsible for designing, building, establishing, and maintaining all kinds of mechanical machinery, tools, and components in the construction industry.

Aerospace industry: Mechanical engineers in aerospace industry produce specifications for design, development, manufacture and installing of new or modified mechanical components or systems. They design more fuel-efficient aircraft that cut emissions and build the fleets of satellites that power modern GPS technology.