Respuesta :
Answer:
R = (18 ± 2) 10¹ Ω
ΔR = 2 10¹ Ω
Explanation:
Ohm's law relates voltage to current and resistance
V = i R
R = [tex]\frac{V}{i}[/tex]V / i
the absolute error of the resistance is
ΔR = | [tex]| \frac{dR}{DV} | \ \Delta V + | \frac{dR}{di} | \ \Delta i[/tex]
the absolute value guarantees the worst case, maximum error
ΔR = [tex]\frac{1}{i} \Delta V+ \frac{V}{i^2} \Delta i[/tex]
The error in the voltage let be approximate, if we use a scale of 10 V, in general the scales are divided into 20 divisions, the error is the reading of 1 division, let's use a rule of direct proportion
ΔV = 1 division = 10 V / 20 divisions
ΔV = 0.5 V
The current error must also be approximate, if we have the same number of divisions
Δi = 50 mA / 20 divisions
Δi = 2.5 mA
let's calculate
ΔR = [tex]\frac{1}{45.5 \ 10^{-3}} \ 0.5 + \frac{8.2}{(45.5 \ 10^{-3})^2 } \ 2.5 \ 10^{-3}[/tex]
ΔR = 10.99 + 9.9
ΔR = 20.9 Ω
The absolute error must be given with a significant figure
ΔR = 2 10¹ Ω
the resistance value is
R = 8.2 / 45.5 10-3
R = 180 Ω
the result should be
R = (18 ± 2) 10¹ Ω
