Question

The current, i, through a resistor is measured with a digital ammeter to be 0.10? The uncertainty in the calculated value of (i^2) will be

Answer 1

Once you have the specific value for the relative uncertainty, you can calculate the uncertainty in
`\(i^2\)` using the formula above.

To find the uncertainty in the calculated value of
`\(i^2\)`, we can use the formula for the relative uncertainty. The relative uncertainty is the ratio of the uncertainty in the result to the value of the result. Mathematically, it's given by:

`\[ \text{Relative Uncertainty} = (\Delta(i^2))/((i^2)) \]`

where
`\(\Delta(i^2)\)` is the uncertainty in the calculated value of
`\(i^2\)`.

Now, let's use the given information. The current
`\(i\)`is measured with an uncertainty
`\(\Delta i\)` of 0.10 A. The calculated value is
`\(i^2\)`.

`\[ i^2 = (0.10 \, \text{A})^2 = 0.01 \, \text{A}^2 \]`

Now, let's find the relative uncertainty:

`\[ \text{Relative Uncertainty} = (\Delta(i^2))/((i^2)) \]`

`\[ \Delta(i^2) = \text{Relative Uncertainty} * (i^2) \]`

To proceed further, we need the specific value of the relative uncertainty. If the relative uncertainty is given as a percentage, you would convert it to a decimal by dividing by 100.

For example, if the relative uncertainty is 2%, you would use
`\( \text{Relative Uncertainty} = 0.02 \)`.

Once you have the specific value for the relative uncertainty, you can calculate the uncertainty in
`\(i^2\)` using the formula above.