FYKOS Year 35 Series 5 Problem 5 — alternating triangle · FYKOS 35 #35.5.5

Physics · mechanics · electromagnetism

Problem

Let us construct the finite Sierpiński triangle of a degree

N

(for

N = 1

it is a single triangle, in case of

N = 2

it is four triangles, etc.). The bases of small triangles (that the Sierpiński triangle is made of) consist of a resistor with resistance

R = 150\,\mathrm{\Omega}

, the left legs are coils of inductance

L = 0.4\,\mathrm{H}

and the other legs are capacitors of capacitance

C = 20\,\mathrm{\upmu{}F}

. We measure the impedance between the triangle's bottom left and right corners. The angular frequency of the source is

\omega = 50\,\mathrm{s^{-1}}

. Find the recurrent relation for the measured impedance and find its value for

N = 7

. What does the recurrent formula looks like if we replace coils and capacitors with resistors

R

? Determine its numerical value for

N = 15

. Schéma obvodu.