The mesh equations (or node equations) needed to solve for the response of any circuit –
memoryless or dynamic – are obtained by applying Kirchhoff’s Voltage Law in meshes (or
Kirchhoff’s Current Law at nodes) along with the element equations. The element equation
of an inductor is and that of a capacitor is There fore, the mesh
equations (node equations) describing a dynamic circuit will be integro-differential
equations. These equations are true for all t,since they are obtained from KVL and KCL that
are true on an instant-to-instant basis. Therefore, both sides of such integro-differential
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