The combined resistance of R of two resistors R1 AND R2 ; where R1;R2 0 is given by 1R = - Maths - Application of Derivatives

Question

The combined resistance of R of two resistors R1 AND R2 ; where
R1;R2>0 is given by 1R = 1/R1+1/R2 IF R1 +R2 = c ; show that
maximum resistance ; R is obtained by choosing R1=R2

Garima Singhal · Accepted Answer

We have,R1 + R2 = C⇒R2 = C - R1    
1now,   1R = 1R1 + 1R2⇒R = R1R2R1+R2⇒R = R1C-R1R1 + C- R1  Using 1⇒R =R1 - R12C⇒dRdR1 = 1 - 2R1Cfor maxima or minima, we havedRdR1 = 01 - 2R1C = 0⇒R1 = C2d2RdR1 = -2C <0So, R is maximum, when R1 = C2now, R2 - C - R1 = C - C2 = C2So, R is maximum, when R1 = R2

The combined resistance of R of two resistors R1 AND R2 ; where R1;R2>0 is given by 1R = 1/R1+1/R2 . IF R1 +R2 = c ; show that maximum resistance ; R is obtained by choosing R1=R2 .