Question

Дано: U1=10; 10,5; 10,4; 9,8; 10,3 В U2=8,6; 8,7; 8,5; 8,7; 8,6 В Найти: U - ? ΔU - ?

Answer 1

U=U1+U2=18,6; 19,2; 18,9; 18,5; 18,9 В

ΔU= U2-U1=-1,4; -1,8; -1,9; -1,1; -1,7 В

Answer 2

Based on the information provided, it appears that U1 and U2 represent two sets of voltage measurements. To find the total voltage U and its uncertainty ΔU, we need to perform some calculations.

1. Finding U: The total voltage U is the average (mean) of the values in each set. To calculate it, add all the values in each set and then divide by the number of values in that set.

For U1: U1 = (10 + 10.5 + 10.4 + 9.8 + 10.3) / 5 = 50 / 5 = 10.0

For U2: U2 = (8.6 + 8.7 + 8.5 + 8.7 + 8.6) / 5 = 42.1 / 5 = 8.42

So, U1 = 10.0 and U2 = 8.42.

2. Finding ΔU: The uncertainty (standard deviation) of each set will give us ΔU1 and ΔU2. To calculate the uncertainty, first, find the mean (average) of the values in each set, then subtract that mean from each value, square the differences, find the average of the squared differences, and finally, take the square root.

For U1: Mean of U1 values = (10 + 10.5 + 10.4 + 9.8 + 10.3) / 5 = 50 / 5 = 10.0

Now, find the differences and square them: (10 - 10.0)^2 = 0 (10.5 - 10.0)^2 = 0.25 (10.4 - 10.0)^2 = 0.16 (9.8 - 10.0)^2 = 0.04 (10.3 - 10.0)^2 = 0.09

Average of squared differences: (0 + 0.25 + 0.16 + 0.04 + 0.09) / 5 = 0.09

Take the square root of the average: ΔU1 = √0.09 ≈ 0.3

For U2: Mean of U2 values = (8.6 + 8.7 + 8.5 + 8.7 + 8.6) / 5 = 42.1 / 5 = 8.42

Now, find the differences and square them: (8.6 - 8.42)^2 ≈ 0.0324 (8.7 - 8.42)^2 ≈ 0.0784 (8.5 - 8.42)^2 ≈ 0.0064 (8.7 - 8.42)^2 ≈ 0.0784 (8.6 - 8.42)^2 ≈ 0.0324

Average of squared differences: (0.0324 + 0.0784 + 0.0064 + 0.0784 + 0.0324) / 5 ≈ 0.0456

Take the square root of the average: ΔU2 = √0.0456 ≈ 0.21

So, ΔU1 ≈ 0.3 and ΔU2 ≈ 0.21.

Therefore, the total voltage U is 10.0, and the uncertainties are ΔU1 ≈ 0.3 and ΔU2 ≈ 0.21.