Question

A student has to measure several unknown charges Q on a capacitor by discharging it through a ballistic galvanometer. The discharge kicks the galvanometer's needle, whose resulting maximum swing tells the student the value of Q. Before making all her measurements, the student wants to know how reliably she can read the maximum displacement of the swinging needle. Therefore, she arranges to charge the capacitor to exactly the same voltage (and hence the same charge) five times and to measure the resulting charge. Her results (in microcoulombs) are:

1.2, 1.4, 1.6, 1.6, 1.2.

Based on these results, what would you suggest she take for the uncertainty δQ in her subsequent measurement of the charge Q, assuming she wants to be 68% confident that the correct value is within +/- δQ of her measurement?

note: compute the individual standard deviation

Answer 1

The readings of the charge are

The uncertainty in the measurement of charge can be calculated by following method

Step 1

Calculate the average of the data

Step 2.

Standard deviation for individual reading

Standard deviation=average - individual charge

Step 3

Calculating mean standard deviation

Mean standard deviation is the uncertainty in this case.

With this uncertainty no readings in the given set can be said to be confidently placed inside the domain of uncertainty.

If she wants to be 68% confident,then at least 4 of her readings should be within the limit of uncertainty allowed by this calculation. Therefore 0.2\mu C must be the uncertainty required to get 68% confidence. Therefore