Two resistances are measured in ohm and are given as: R1=3 Ω ±1 % R2=6 Ω ±2 % When they are connected in parallel, the percentage error in equivalent resistance is

Question

Two resistances are measured in ohm and are given as: R1=3 Ω ±1 % R2=6 Ω ±2 % When they are connected in parallel, the percentage error in equivalent resistance is (A) 3 % (B) 4.5 % (C) 0.67 % (D) 1.33 %

Tardigrade Admin · Accepted Answer

(1/Re q)=(1/R1)+(1/R2) (d Re q/R2)=(d R1/R12)+(d R2/R22)⇒ (d Re q/Re q)=((d R1/R12) + (d R2/R22))× Re q ⇒ ((1/3) + (2/6))× 2 ⇒ ∴ % error =(4/3) %

Q. Two resistances are measured in ohm and are given as:

$R_{1} = 3 Ω \pm 1%$

$R_{2} = 6 Ω \pm 2%$

When they are connected in parallel, the percentage error in equivalent resistance is

$3%$

$4.5%$

$0.67%$

$1.33%$

Q. Two resistances are measured in ohm and are given as: R1​=3Ω±1% R2​=6Ω±2% When they are connected in parallel, the percentage error in equivalent resistance is

3%

4.5%

0.67%

1.33%

Req​1​=R1​1​+R2​1​ R2dReq​​=R12​dR1​​+R22​dR2​​⇒Req​dReq​​=(R12​dR1​​+R22​dR2​​)×Req​ ⇒(31​+62​)×2 ⇒∴% error =34​%

Q. Two resistances are measured in ohm and are given as:

$R_{1} = 3 Ω \pm 1%$

$R_{2} = 6 Ω \pm 2%$

When they are connected in parallel, the percentage error in equivalent resistance is

$3%$

$4.5%$

$0.67%$

$1.33%$