0:00
Hi.
00:02
So in this question we have to combine two uncertainties in two values that we measured to get the uncertainty in a quantity that we derived from the measured quantities.
00:17
More specifically we have a resistor with some resistance r and we measure the current i that flows to the resistor and we also measured the voltage v across the resistor.
00:28
We know the value of the current that we measure, so 0 .99 plus minus 0 .02 amps.
00:37
So this means that the uncertainty in the current is 0 .02.
00:43
And we also know the measured value of the voltage 3 .23 plus minus 0 .01 volts.
00:51
So the uncertainty in the voltage is 0 .01.
00:56
Now we have to calculate the uncertainty in the resistance and let's call this uncertainty delta r.
01:08
Okay, so i will be using this greek letter delta to to symbolize the uncertainty in the quantity are.
01:19
Okay, so let's start with the relation between the voltage current and the resistance and this is given by oms law, which tells us that the resistance is the ratio between the voltage across the resistor and the current flowing through the resistor.
01:35
When we have such a ratio as the one on the right -hand side of the equation, we have to apply the so -called the rule of adding uncertainties in quadrature.
01:55
So the keyword here is quadrature.
01:59
And this rule can usually be found in the appendix of the physics textbook.
02:05
So this rule tells us that in order to get the relative uncertainty in r, so what does the relative means, so the relative means that we have to divide the absolute uncertainty by the value of the resistance.
02:21
Okay, so this is the relative uncertainty or relative error.
02:32
So in order to calculate this relative uncertainty, we have to use the relative uncertainty in the current, which we have measured, and the relative uncertainty in the voltage, which we also have measured...