A simpler derivation of the integral formula of electrical resistance

The proportionality constant in Ohm's law is the electrical resistance. The resistance of conducting objects depends on their geometrical features such as cross-sectional area and length. Since the cross-sectional area of resistors usually varies as its length, the calculation of resistances is a non-trivial task. In this letter, a closed-form integral expression for resistance is just derived for resistors with parallel curved terminals. The derivation proposed here, equally applicable to the calculation of capacitances, uses the properties of an electric field and the mathematical concept of parallel surfaces. This new teaching strategy can be useful for first undergraduate courses of science and engineering studies. (letters and comments)