Analogu3 Beat

2021 Solution 09

Isaac P Abraham
2020 Dec 25

Consider the following circuit with two parallel bulbs.

The following transformations are easy to follow.

I

0

=

I

1

+

I

2

(

1

)

Multiply both sides with

(

I

0

-

I

1

)

to result in,

I

1

I

0

-

2

I

1

+

I

0

I

2

-

I

1

I

2

=

2

I

0

-

I

0

I

1

(

2

)

Transpose the third term from the left hand side to the right hand side.

I

1

I

0

-

2

I

1

-

I

1

I

2

=

2

I

0

-

I

0

I

1

-

I

0

I

2

(

3

)

Factor

I

1

from the left hand side and

I

0

from the right hand side to get,

I

1

(

I

0

-

I

1

-

I

2

)=

I

0

(

I

0

-

I

1

-

I

2

)

(

4

)

Divide both side by the bracketed term that is common on both sides. We now have,

I

1

=

I

0

!

(

5

)

It is also possible to show that

I

2

=

I

0

if we have multiplied the initial equation with

(

I

0

-

I

2

)

. How can we explain the result?

At equation (4), we generated

0=0

and them proceed to implement an invalid division by zero to arrive at (5).

Ref: Valerii Ilyushchenko (translated by V.N. Lange), "Science for everyone", Mir Publishers, Moscow, USSR.