Create a detailed, close-up image of a resistance box. It should be a scientific instrument with several adjustable dials and assorted resistors, each one clearly visible and labeled with their respective values and tolerances. Each resistor should be visually distinct and identifiable, representing the variety of physical properties in electronic components. The background of the box should be neutral to emphasize the resistors and their markings.

A resistance box has the following components and tolerances:

10 resistors each of 100k§Ù ¡¾ 0.05%
10 resistors each of 10k§Ù ¡¾ 0.05%
10 resistors each of 1k§Ù ¡¾ 0.05%
10 resistors each of 100§Ù ¡¾ 0.1%
10 resistors each of 10§Ù ¡¾ 0.5%

Determine both in ohms and percentage the limit of uncertainty in setting of 453.72k§Ù

first, calculate the additive errors.

4x100k error is 400Kx.0005=200
5x10k error is 50kx.0005=25
3x1k error is 3kx.0005=1.5ohm
7x100 error is 700x.001=.7
2x10 error is 20x.005=.1 ohm

error^2=200^2+25^2+1.5^2+.7^2 +.1^2
do the math, that is the error in ohms. Then figure percent.

limit of uncertainity is harder. Notice your percents are to one significant figure, so 200 in the first one can range from 150 to 250. all the others are withing that error, so you have +-250 ohm. Your instructor may have given you other instructions on this. If the percent error was to be considered absolute, then add the errors.

Well, well, well, looks like someone is trying to give the resistance box a hard time, huh? Don't worry, I'm here to help you figure out the uncertainty in setting that tricky value of 453.72kΩ.

Let's break it down, shall we?

First, let's determine the values and tolerances of the components that make up this value.

453.72kΩ is made up of:

4 resistors of 100kΩ ± 0.05%

5 resistors of 10kΩ ± 0.05%

3 resistors of 1kΩ ± 0.05%

No resistors of 100Ω ± 0.1% or 10Ω ± 0.5% are needed to achieve this value.

Now, let's calculate the uncertainty based on these components:

Uncertainty in resistance = (Total tolerance / 100) * Nominal resistance

For the 100kΩ resistors: (0.05 / 100) * 100kΩ = 50Ω

For the 10kΩ resistors: (0.05 / 100) * 10kΩ = 5Ω

For the 1kΩ resistors: (0.05 / 100) * 1kΩ = 0.5Ω

No contribution from the 100Ω or 10Ω resistors.

Now, let's add up these uncertainties:

Total uncertainty = uncertainty from 100kΩ resistors + uncertainty from 10kΩ resistors + uncertainty from 1kΩ resistors

Total uncertainty = 50Ω + 5Ω + 0.5Ω = 55.5Ω

So, the limit of uncertainty in setting 453.72kΩ is 55.5Ω.

Now, if we want to calculate the percentage uncertainty, we can use the following formula:

Percentage uncertainty = (Total uncertainty / Nominal resistance) * 100

Percentage uncertainty = (55.5Ω / 453.72kΩ) * 100 = 0.0122%

So, the limit of uncertainty in setting 453.72kΩ is approximately 55.5Ω (or 0.0122%).

Hope this helps, and remember, uncertainty is just a part of life, like a clown at a birthday party!

To determine the limit of uncertainty in setting a resistance of 453.72kΩ, we need to consider the tolerances of the individual resistors used in the resistance box.

For a resistance of 453.72kΩ, we would need to use the 100kΩ resistors. Since each of these resistors has a tolerance of ±0.05%, we can calculate the limit of uncertainty as follows:

Upper limit of uncertainty: 453.72kΩ + (453.72kΩ x 0.05%) = 453.72kΩ + (453.72kΩ x 0.0005) = 453.72kΩ + 227.86Ω = 454kΩ (rounded to the nearest whole number)

Lower limit of uncertainty: 453.72kΩ - (453.72kΩ x 0.05%) = 453.72kΩ - (453.72kΩ x 0.0005) = 453.72kΩ - 227.86Ω = 453kΩ (rounded to the nearest whole number)

Therefore, the limit of uncertainty in setting a resistance of 453.72kΩ using the 100kΩ resistors is between 453kΩ and 454kΩ.

In terms of percentage, the upper limit of uncertainty is calculated as (454kΩ - 453.72kΩ) / 453.72kΩ x 100% = 0.06% (rounded to two decimal places). The lower limit of uncertainty is calculated as (453.72kΩ - 453kΩ) / 453.72kΩ x 100% = 0.16% (rounded to two decimal places).

Therefore, the percentage limit of uncertainty in setting a resistance of 453.72kΩ using the 100kΩ resistors is between 0.06% and 0.16%.

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%.