To determine the limit of uncertainty in setting the resistance of 453.72kΩ, we need to calculate the highest and lowest possible values within the given tolerances for each component.
Let's start by calculating the range of resistance values for each component:
For the 100kΩ resistors with a tolerance of ±0.05%:
Range = 100kΩ * 0.05% = 50Ω
Therefore, the resistance range for these resistors is 100kΩ ± 50Ω.
For the 10kΩ resistors with a tolerance of ±0.05%:
Range = 10kΩ * 0.05% = 5Ω
Therefore, the resistance range for these resistors is 10kΩ ± 5Ω.
For the 1kΩ resistors with a tolerance of ±0.05%:
Range = 1kΩ * 0.05% = 0.5Ω
Therefore, the resistance range for these resistors is 1kΩ ± 0.5Ω.
For the 100Ω resistors with a tolerance of ±0.1%:
Range = 100Ω * 0.1% = 0.1Ω
Therefore, the resistance range for these resistors is 100Ω ± 0.1Ω.
For the 10Ω resistors with a tolerance of ±0.5%:
Range = 10Ω * 0.5% = 0.05Ω
Therefore, the resistance range for these resistors is 10Ω ± 0.05Ω.
Now, let's calculate the total resistance range by considering the 10 resistors of each type:
For the 100kΩ resistors:
Highest value = (100kΩ + 50Ω) * 10 = 1,050kΩ
Lowest value = (100kΩ - 50Ω) * 10 = 950kΩ
For the 10kΩ resistors:
Highest value = (10kΩ + 5Ω) * 10 = 150kΩ
Lowest value = (10kΩ - 5Ω) * 10 = 50kΩ
For the 1kΩ resistors:
Highest value = (1kΩ + 0.5Ω) * 10 = 15.5kΩ
Lowest value = (1kΩ - 0.5Ω) * 10 = 9.5kΩ
For the 100Ω resistors:
Highest value = (100Ω + 0.1Ω) * 10 = 1.001kΩ
Lowest value = (100Ω - 0.1Ω) * 10 = 0.99kΩ
For the 10Ω resistors:
Highest value = (10Ω + 0.05Ω) * 10 = 100.5Ω
Lowest value = (10Ω - 0.05Ω) * 10 = 99.5Ω
Now, let's calculate the total resistance range for the resistance box:
Highest value = 1,050kΩ + 150kΩ + 15.5kΩ + 1.001kΩ + 100.5Ω = 1,317.001kΩ
Lowest value = 950kΩ + 50kΩ + 9.5kΩ + 0.99kΩ + 99.5Ω = 1,109.99kΩ
Therefore, the limit of uncertainty in setting the resistance of 453.72kΩ using this resistance box is:
Highest value = 1,317.001kΩ - 453.72kΩ = 863.281kΩ
Lowest value = 453.72kΩ - 1,109.99kΩ = -656.27kΩ
However, a negative resistance value doesn't make sense, so we consider the lowest value as 0. This means the limit of uncertainty in setting the resistance of 453.72kΩ is from 0 to 863.281kΩ.
To calculate the limit of uncertainty in percentage, we need to divide the range by the target value (453.72kΩ):
Percentage uncertainty = (Range / Target resistance) * 100
For the highest value:
Percentage uncertainty = (863.281kΩ / 453.72kΩ) * 100 = 190.37%
For the lowest value:
Percentage uncertainty = (0 / 453.72kΩ) * 100 = 0%
Therefore, the limit of uncertainty in percentage when setting the resistance of 453.72kΩ using this resistance box is from 0% to 190.37%.