Source: Extra Practice

Two resistors are connected in series. Their resistances are R1=(100±3)ΩR_1 = (100 \pm 3) \Omega and R2=(200±4)ΩR_2 = (200 \pm 4) \Omega. What is the equivalent resistance ReqR_{eq} with its associated error?

Options

Option A

(300±1)Ω(300 \pm 1) \Omega

Option B

(300±3.5)Ω(300 \pm 3.5) \Omega

Option C is correct

(300±7)Ω(300 \pm 7) \Omega

Option D

(300±5)Ω(300 \pm 5) \Omega

Explanation

When quantities are added or subtracted, their absolute errors add up. For resistors in series, the equivalent resistance is Req=R1+R2R_{eq} = R_1 + R_2. Mean value of Req=100Ω+200Ω=300ΩR_{eq} = 100 \Omega + 200 \Omega = 300 \Omega . The maximum possible absolute error in the sum is the sum of the individual absolute errors: ΔReq=ΔR1+ΔR2=3Ω+4Ω=7Ω\Delta R_{eq} = \Delta R_1 + \Delta R_2 = 3 \Omega + 4 \Omega = 7 \Omega. Therefore, the equivalent resistance is (300±7)Ω(300 \pm 7) \Omega.