If two resistors with resistances R1 and R2 are connected in parallel, then the total resistance R measured in ohms is given by 1/R= 1/R1 + 1/R2If R1 is increasing at a rate of 0.3 ohms/second and...

If two resistors with resistances R1 and R2 are connected in parallel, then the total resistance R measured in ohms is given by 1/R= 1/R1 + 1/R2

If R1 is increasing at a rate of 0.3 ohms/second and R2 is increasing at a rate of 0.2 ohms/second, how fast is R changing when R1=80 ohms and R2=100 ohms?

Asked on by toby712

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equivalent resistance of two resistances connected in parallel is given by `1/R = 1/R1 + 1/R2`

`R = (R1*R2)/(R1 + R2)`

`(dR)/(dt) = ((R1*(dR2)/dt + R2*(dR1)/dt)(R1 + R2) - (R1*R2*((dR1)/dt + (dR2)/dt)))/(R1 + R2)^2`

R1 is increasing at a rate of 0.3 ohms/second and R2 is increasing at a rate of 0.2 ohms/second, when R1 = 80 ohms and R2 =100 ohms,

=> `(dR)/(dt) =( (80*0.2 + 100*0.3)*180 - (8000*(0.3 + 0.2)))/180^2`

=> `(dR)/dt = 0.132` ohm/second

The equivalent resistance is changing at 0.132 ohm/second

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