FOCUS ON MATH

Integral Voltage-Current Relationships

The inductance may be defined by the voltage-current relationship

Re-writing the above Equation

We apply integration. Let us consider the limits to be placed on the two integrals. The lower limit may be assumed as current at initial time I (t0), therefore

 (13.5)

By solving the above equation, we have

 (13.6)

or

 (13.7)

We may write the integral as an indefinite integral and include a constant of integration k

 (13.8)

where the constant of integration depends on the initial conditions (t = 0). The power absorbed in the inductor is given by

 

               

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