Question

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

Answer 1

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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