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A metal microelectrode has a tip that can be modeled as being cylindrical. The metal itself is 1X10^-6m in diameter, adn the tip region is 3mm long. The metal insulation material 0.2 x10^-6 m thick. The insulation material has a relative dielectric constant of 1.67. Only the base of the cylinder is free of insulation. What is the resistance associated with the tip of this microelectrode

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Answer:

Resistance   =1.27*10¹¹

Explanation:

Given Data:

Diameter (d) = 1X10^-6m

Length (L) = 3mm = 0.003m

Thickness = 0.2 x10^-6 m

Dielectric constant = 1.67

Resistivity = 10^3 Ohms/cm²

Calculating the cross sectional area, we have

A = πd²/4

   = π*(1*10⁻⁶)²/4

    =3.142*10⁻¹²/4

     = 7.855 *10⁻¹³ m²  = 7.855 *10⁻⁹cm²

Calculating resistance using the formula;

R = Rs/A

  = 1000/7.855 *10⁻⁹

  =1.27*10¹¹