Answer:
a) The uncertainty in calculated V, ΔV = 25.3
b) The uncertainty in calculated v, Δv = 0.41 m/s
c) The uncertainty in calculated V, ΔV = 22.2 V
Explanation:
We'll use Upper-Lower Bounds method of uncertainty to estimate the uncertainties.
a) I = 5.1 A, ΔI = 0.3 A
I = (5.1 ± 0.3) A
R = 77.5 ohms, ΔR = 0.4 ohms
R = (77.5 ± 0.4) ohms
V = IR = 5.1 × 77.5 = 395.25 V
The lower bound for the voltage will be calculated using the lower bounds for the current and resistance
Iₗ = 5.1 - 0.3 = 4.8 A
Rₗ = 77.5 - 0.4 = 77.1 ohms
Vₗ = 4.8 × 77.1 = 370.08 V
The upper bound for the voltage will be calculated using the upper bounds for the current and resistance
Iᵤ = 5.1 + 0.3 = 5.4 A
Rᵤ = 77.5 + 0.4 = 77.9 ohms
Vᵤ = 5.4 × 77.9 = 420.66 V
The average of the differences from the mean voltage/true value is 25.3 V
V = 395.25 V, Δ = 25.3V
V = (395.25 ± 25.3) V
b) x = 2.9 m, Δx = 0.3 m
x = (2.9 ± 0.3) m
t = 4.4 s, Δt = 1.8 s
t = (4.4 ± 1.8) ohms
v = x/t = 2.9/4.4 = 0.659 m/s
The lower bound for average speed will be calculated using the lower bounds for distance and upper bounds for time.
xₗ = 2.9 - 0.3 = 2.6 m
tᵤ = 4.4 + 1.8 = 6.2 s
vₗ = 2.6/6.2 = 0.419 m/s
The upper bound for the average speed will be calculated using the upper bound for the distance and lower bound for time
xᵤ = 2.9 + 0.3 = 3.2 m
tₗ = 4.4 - 1.8 = 2.6 s
vᵤ = 3.2/2.6 = 1.231 m/s
The average of the differences from the mean average speed/true value is 0.41 m/s
v = 0.659 m/s, Δv = 0.41 m/s
v = (0.659 ± 0.41) m/s
c) ) I = 9.8 A, ΔI = 0.5 A
I = (9.8 ± 0.5) A
R = 40.5 ohms, ΔR = 0.2 ohms
R = (40.5 ± 0.2) ohms
V = IR = 9.8 × 40.5 = 396.9 V
The lower bound for the voltage will be calculated using the lower bounds for the current and resistance
Iₗ = 9.8 - 0.5 = 9.3 A
Rₗ = 40.5 - 0.2 = 40.3 ohms
Vₗ = 9.3 × 40.3 = 374.79 V
The upper bound for the voltage will be calculated using the upper bounds for the current and resistance
Iᵤ = 9.8 + 0.5 = 10.3 A
Rᵤ = 40.5 + 0.2 = 40.7 ohms
Vᵤ = 10.3 × 40.7 = 419.21 V
The average of the differences from the mean voltage/true value is 22.2 V
V = 396.9 V, Δ = 22.2 V
V = (396.9 ± 22.2) V
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