Login

Two resistors of resistances R ₁ = 100+/- 3 ohm and R₂= 200 +/- 4 ohm are connected (a) in series, (b) in parallel. Find the equivalent resistance of the (a) series combination, (b) parallel combination. Use for (a) the realtion R = R₁+ R₂and for (b) 1/R ' = 1/R₁+ 1/R₂and ΔR '/R '²= ΔR₁/R₁ ²+ ΔR₂/R₂ ².

$R_{1} = 100 \pm 3 R_{2} = 200 \pm 4 R_{s e r i e s} = R_{1} + R_{2} + Δ R_{s e r i e s} Δ R_{s e r i e s} = Δ R_{1} + Δ R_{2} = \frac{3}{100} \times 100 + \frac{4}{200} \times 100 = 3 % + 2 % = 5 % R_{s e r i e s} = 300 \pm 5 % R_{p a r a l l e l} = \frac{R_{1} R_{2}}{R_{1} + R_{2}} = \frac{100 \times 200}{100 + 200} = \frac{200}{3} \frac{Δ R_{p a r a l l e l}}{R_{p a r a l l e l}^{2}} = \frac{Δ R_{p a r a l l e l}}{(\frac{200}{3})^{2}} \frac{Δ R_{1}}{R_{1}^{2}} + \frac{Δ R_{2}}{R_{2}^{2}} = \frac{3 %}{100^{2}} + \frac{2 %}{200^{2}} Δ R_{p a r a l l e l} = \frac{4}{9} (3 % + 0.5 %) = 1.55 % R_{p a r a l l e l} = \frac{200}{3} \pm 1.55 %$

-89

View Full Answer

Copyright © 2024 Aakash EduTech Pvt. Ltd. All rights reserved.

Aakash EduTech Pvt. Ltd.

What are you looking for?