Question

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

Answer 1

Resistance =1.27*10¹¹

Step-by-step 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