Two resistors $\mathrm{R}_{1}=(4 \pm 0.8) \Omega$ and $\mathrm{R}_{2}=(4 \pm 0.4) \Omega$ are connected in parallel. The equivalent resistance of their parallel combination will be:

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Units & Measurement

Two resistors

R_{1} = (4 \pm 0.8) Ω

and

R_{2} = (4 \pm 0.4) Ω

are connected in parallel. The equivalent resistance of their parallel combination will be:

Answer: (B)

The parallel value is

R_{e q} = \frac{R _{1} R _{2}}{R _{1} + R _{2}} = \frac{4 \times 4}{8} = 2 Ω

. Differentiating

\frac{1}{R _{e q}} = \frac{1}{R _{1}} + \frac{1}{R _{2}}

, the absolute error is

Δ R_{e q} = R_{e q}^{2} (\frac{Δ R _{1}}{R _{1}^{2}} + \frac{Δ R _{2}}{R _{2}^{2}}) = 4 (\frac{0.8}{16} + \frac{0.4}{16}) = 4 \times 0.075 = 0.3 Ω

. The equivalent resistance is

(2 \pm 0.3) Ω

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Single correct option