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By Xuan Herrera

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Further, the current only increases significantly if the applied voltage is positive, not negative. The ratio V/I for some point along the nonlinear curve is sometimes called the static, or chordal, or DC, resistance , but as seen in the figure the value of total V over total I varies depending on the particular point along the nonlinear curve which is chosen. This means the "DC resistance" V/I at some point on the curve is not the same as what would be determined by applying an AC signal having peak amplitude ΔV volts or ΔI amps centered at that same point along the curve and measuring ΔV/ΔI.

The ratio V/I for some point along the nonlinear curve is sometimes called the static, or chordal, or DC, resistance , but as seen in the figure the value of total V over total I varies depending on the particular point along the nonlinear curve which is chosen. This means the "DC resistance" V/I at some point on the curve is not the same as what would be determined by applying an AC signal having peak amplitude ΔV volts or ΔI amps centered at that same point along the curve and measuring ΔV/ΔI.

Here is the argument more specifically: The integral form of Gauss's law is: for any closed surface S containing charge Q. By the divergence theorem, this equation is equivalent to: for any volume V containing charge Q. By the relation between charge and charge density, this equation is equivalent to: for any volume V. In order for this equation to be simultaneously true for every possible volume V, it is necessary (and sufficient) for the integrands to be equal everywhere. Therefore, this equation is equivalent to: Thus the integral and differential forms are equivalent.

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