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Two resistances R1 = (16 +- 0.3) ohm and...

Two resistances `R_1 = (16 +- 0.3) ohm and R_2 = (48 +- 0.5) ohm` are connected in parallel. Find the total resistance of the combination and maximum percentage error.

Text Solution

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Here, `R_1 = 16 ohm, Delta R_1 = 0.3 Omega`
`R_2 = 48 ohm, DeltaR_2 =0.5 Omega, R_p = ?`
`(1)/(R_p) = (1)/(R_1) +(1)/(R_2) = (1)/(16) +(1)/(48) = (3+1)/(48) = (4)/(48) = (1)/(12)`
`R_p = 12 ohm`
On differentating, `(1)/(R_p) = (1)/(R_1) +(1)/(R_2)`, we get `(-DeltaR_p)/(R_p^2) = - (DeltaR_1)/(R_1^2) - (DeltaR_2)/(R_2^2)`
`:. DeltaR_p = DeltaR_1((R_p)/(R_1))^2 + DeltaR_2((R_p)/(R_2))^2 = 0.3((12)/(16))^2 +0.5((12)/(48))^2`
= `0.16875+0.03125 = 0.20 ohm`
`(DeltaR_p)/(R_p)xx10 = (0.20)/(12)xx100 = 1.6%`
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