Question

1. Determine the current l, when Vs = 12 V as shown in the figure below
ΣΩ
ΛΑ
8 Ω
ΜΜΜ
αν
+ ,
1,
4Ω
Ω
622
Α.​

Answer 1

Here,

Let X be the equivalent resistance of the infinite network

This network consists of infinite sets of three resistors of 1Ω,1Ω and adding one more set across AB to he infinite network will not affect the equivalent resistance.

We know that

Resistance between A and B

R

p

=

x+1

x

(∴

R

1

=

x

1

+

1

1

)

R

s

=1+

x+1

x

+1=2+

x+1

x

This must be equal to the initial resistance x

∴x=2+

x+1

x

⇒x+x

2

=2+2x+x

⇒x

2

−2x−2=0

⇒x=

2

2±

4+8

=1±

3

But x



=1−

3

∴x=(1+

3

)Ω

=2.732Ω

Current I=

Total resistance

e.m.f

=

2.732+0.5

12

I=3.7A