Couple of uncertainty questions

[nugget]

1. The area of a circle has a fractional uncertainty of 0.08 (i.e. 8%), what is the fractional uncertainty of it's radius?

So i suppose you have to use A = pi(r^2) and rearrange, bit confused though...

2. Square wave has a height of 2.4cm +/- 0.2cm. This signal is applied across a resistor of R = 10.0 +/- 0.2 ohm. What is the fractional uncertainty in the heating power dissipated by the resistor?

Figured this is the right formula... P = (V^2)/R

again a bit unsure how to do it.

thanks

 

[berkeman]

1. The area of a circle has a fractional uncertainty of 0.08 (i.e. 8%), what is the fractional uncertainty of it's radius?

So i suppose you have to use A = pi(r^2) and rearrange, bit confused though...

2. Square wave has a height of 2.4cm +/- 0.2cm. This signal is applied across a resistor of R = 10.0 +/- 0.2 ohm. What is the fractional uncertainty in the heating power dissipated by the resistor?

Figured this is the right formula... P = (V^2)/R

again a bit unsure how to do it.

thanks

As you should know, we don't do your work for you. How should you use uncertainties and those formulas to calculate the final uncertainties? If the equation is linear, the transfer of the uncertainty depends on what? If the equation is non-linear, the uncertainty depends on what? Read your textbook...

 

[tomcue]

I can provide a response to these uncertainty questions. For the first question, the fractional uncertainty of the radius can be calculated using the formula for the area of a circle, A = πr^2. We can rearrange this formula to solve for the radius, r = √(A/π). Then, we can substitute the fractional uncertainty of the area (0.08) into the equation to find the fractional uncertainty of the radius, which would be 0.04 or 4%.

For the second question, we can use the formula for power dissipated by a resistor, P = (V^2)/R. Here, we can rearrange the formula to solve for the voltage, V = √(PR). Then, we can substitute the fractional uncertainty of the square wave height (0.2) and resistor value (0.02) into the equation to find the fractional uncertainty of the voltage. We can then use this value to calculate the fractional uncertainty of the power dissipated by the resistor. This would require more information, such as the actual voltage and power values, to provide an accurate answer. However, the process would be similar to the first question by substituting the fractional uncertainties into the equation and calculating the final result.