Class 12 NEET Physics Current Electricity Questions Part 1

Let x be resistance per unit length of the wire. Then,
the resistance of the upper portion is, R1=xl1
the resistance of the lower portion is, R2=xl2
Equivalent resistance between A and B is
R=

R1R2

R1+R2

=

(xl1)(xl2)

xl1+xl2

8

3

=

xl1l2

l1+l2

or

8

3

=

xl1l2

l2( l1 l2 +1)

or

8

3

=

xl1

( l1 l2 +1 )

......(i)
(i)Also R0=xl1+xl2
12=x(l1+l2)
12=xl2(

l1

l2

+1) .....(ii)
Divide (i) by (ii), we get

8 3

12

=

xl1 ( l1 l2 +1)

xl2( l1 l2 +1)

or

8

36

=

l1

l2( l1 l2 +1)2

(

l1

l2

+1)2

8

36

=

l1

l2

or (

l1

l2

+1)2

2

9

=

l1

l2

Let y=

l1

l2

∴ 2(y+1)2=9y or 2y2+2+4y=9y
or 2y2−5y+2=0
Solving this quadratic equation, we get
y=

1

2

or 2∴

l1

l2

=

1

2