An infinite resistor network is shown below, composed of resistors of resistance
ID: 2261589 • Letter: A
Question
An infinite resistor network is shown below, composed of resistors of resistance R0 on
the horizontal wires, and 2R0 on the vertical wires.
a) (2pt) Draw a simplified version of the given network that will enable you to compute
the equivalent resistance (Req) for the whole infinite network
b) (5pt) What is the equivalent resistance Req, in terms of R0
c) (7pt) Assume the current coming into the network is i0, what is the horizontal current
i1, that comes out of the first T-junction, as shown in the picture below?
d) (6pt) What is the horizontal current iN, coming out of the Nth T-junction, as shown in
the picture below?
Explanation / Answer
a) consists of 2R0 horizontal and vertiacal 2R0 parallel with R0+R0sqrt(5)
b) 2R0 + 2R0(R0+R0sqrt(5))/(3R0 + R0sqrt(5))
c) i1 = i0*(2R0/(3R0+R0sqrt(5))
d) iN = i0*(2R0/(3R0+R0sqrt(5))^N