So-called analog computers use circuits to solve mathematical problems, particularly when they involve differential equations. Suppose we are given the following differential equation to solve. dy(t) dt + ay(t) = x(t) In this equation, a is a constant. 1. When the input is a unit step the output is given by (x(t)=u(t)) What is the total energy expended by the input? y(t) = (1-e-(at))u(t)

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Nodal Analysis

In the analysis of any electric circuit, nodal analysis is the method of determining the potential difference or voltage between different nodes in an electric circuit. A node is a point where two or more branches connect each other. In the nodal analysis, the voltages are determined in the terms of branch currents. The nodal analysis is also known as the node voltage method or branch current method. The nodal analysis method is one of the several applications of Kirchhoff's Current Law (KCL).