scaling in electricity || MODULE 3 || EC 465 || KTU MEMS || LECTURE 21

Hi all, today we are going to discuss about scaling in electricity and scaling in fluid flow. First, let's see scaling in electricity. Scaling in electricity means, we are giving power to most of the actuating devices. So, when we reduce the size of the devices, what happens to the power loss? To know all these things, we are studying scaling in electricity. We are discussing how many times the power loss occurs. So, first let's see electric resistance. The equation of electric resistance is R is equal to Rho L by A. So, if we convert this to linear dimension, instead of L, we can write L raised to 1. Instead of A, we can write L square. Rho is the resistivity. Since resistivity is a constant value, we don't have to consider it. So, L is equal to L. A is equal to L divided by L square. So, L divided by L square is equal to L raised to minus 1. This is the meaning. If we reduce the size or length of the elements by 10 times, the resistance becomes L raised to minus 1. Now, let's see the resistive power loss. Before that, there is a correction here. This is Rho. Rho is the symbol of proportionality. Please change that. Now, let's see the resistive power loss. P is equal to V square divided by R. The equation of power is V square divided by R. What is V? V is the applied voltage. Applied voltage is always a constant value. Since it is a constant, we can take it as 1. 1 divided by L raised to minus 1. That is proportional to L raised to 1. Now, let's see the electric field energy. The equation to calculate the electric field energy is U is equal to half epsilon E square. Epsilon is the dielectric permittivity. Epsilon is the electric field strength. Electric field strength is the volt per meter. Volt is not a unit. L is the meter. The unit of electric field strength is L raised to minus 1. Now, let's see the ratio of power loss to available power. Available power is the power used for actuation. Available power is proportional to system volume. Available power is proportional to L cubed. Power divided by available power. Ratio of power loss to available power. Ratio of power to available power is L raised to 1 divided by L cubed. L raised to minus 2. 10 times reduction in size L of the power supply system causes 100 times power loss due to the increase of resistivity.