# the resultant resistance of two resistance wires in series combination is 108 ohm and in parallel combination is 24 ohm. find the value of individual resistance

1
by deepesh08

• Brainly User
2014-06-02T15:40:15+05:30
the resultant resistance of two resistance wires in series combination is 108 ohm and in parallel combination is 24 ohm. find the value of individual resistance?
Solution:
Let the resistances of two wires be r1 and r2 .
According to Question ,
Equivalent  Series resistance = 108
r1+r2 = 108  ........................(1)
Equivalent Parallel resistance  = 24
1/r1+1/r2 = 1/24

r1+r2/r1r2 =1/24
or 24 (r1+r2) = r1r2
Using equation 1 , we get
24(108) = r1r2
2592 = r1r2
or              r1r2 = 2592
or r1 = 2592 /r2    .......................  (2)

Using equation 2 in equation 1 ,we get
2592 /r2 +r2 = 108
2592 +r2² =108r2
r2² - 108r2 +2592 = 0

Now we have to solve the above quadratic equation
here a=1 , b= -108 and c= 2592
d = -b +-√(b² - 4ac)/2a

= -(-108)+-√((-108)² - 4*1*2592) /2*1
=108 +-√(11664 - 10368 ) / 2*1
=108 +-√1296 / 2
=108+-36 /2
= 108+36 / 2 or 108-36/2
= 142 /2 or 72/2
= 71 or 36
Let me take it as 36
hence r2 = 36
Substitute r2 = 36 in equation 1 , we get
r1 +36 = 108
r1 = 108 - 36
r1 = 72

Hence the two resistance are 36 and 72 !!
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