Using a search coil and CRO to investigate the magnetic fields generated by alternating currents (A.C.) through a straight wire and a slinky solenoid.

Relationship between the potential different across the capacitor and the time

From the above V-t graph, the curve is a straight line passes through origin. Hence, the potential difference across the capacitor is directly proportional to the time for the CRO trace to rise in steps of 1V and the slope () which represented the charging rate, is constant.
Relationship between the charge stored in the capacitor and the potential different across it when the charging current is constant

The area of the graph (Vt) represented the charge stored in the capacitor. As the rate of change of potential, it implies the charge stored in the capacitor increase with potential, thus the charge stored in the capacitor directly proportional to the potential difference across the capacitor when the charging current is a constant.

In a mathematic mean,
By the equation I = C ,Given that I and are constant
(where I is the charging current, C is the capacitance and v is the potential difference across the capacitor)
Integrate both sides of the equation with time t,
It show that in time t, Q = CV (where Q is the area of V-t graph)
Hence, the charge stored in the capacitor directly proportional to the potential difference across the capacitor when the charging current is a constant.

Comparing the measured capacitance of the capacitor and the marked valued

The marked capacitance of the capacitor is 470μF.
By the equation I = C where I &  is constant.
Given that the fixed current I is 80μA
and  is 0.0817 by the calculation of the V-t graph,
The measured capacitance: 80÷0.0817= 979μF
The percentage error: ×100％=109％

Sources of Error
1. Random Error
CRO
The CRO is used for the measurement of the potential difference across the capacitor.
The smallest division is 0.1V.
Maximum possible error is ±0.05V
Maximum percentage error of the measurement: × 100% = 5%
Ammeter
The ammeter is used for the measurement of the current passes through the capacitor.
The smallest division is 1μA.
Maximum possible error is ±0.5μA
Maximum percentage error of the measurement: × 100% = 0.625%
Stopwatch
The stopwatch is used for the measurement of the time taken for the CRO trace to rise in steps of 1V .
The smallest division is 0.01s.
Maximum possible error is ±0.005s
Maximum percentage error of the measurement: × 100% = 0.0455%

Improvement
By repeating the measurement in the experiment, the result of the experiment can be more accurate.

2. Systematic Error
Adjustment of current
In the experiment, we need to keep the charging current constant as I, i.e.80μA by hand. However, the rate of the decrease of the current is not constant. When the potential difference across the capacitor becomes larger, the rate of the decrease of the current will increase too. It is difficult to adjust the current constant as I.

Reaction time
We mark the time taken of the CRO trace to rise in steps of 1V. If the reaction time of the timer is large, the measurement will be less accurate. And the average reaction time of human is 0.02s
Hence, Maximum percentage error of the measurement of time: × 100% = 0.227%
Improvement
Both of them can be improved by practicing the task in the experiment.





                            -End of report-