Question

A transformer is a device that takes advantage of Faraday’s Law to change an AC voltage. It consists of a primary coil and a secondary coil. When a transformer is used to raise the voltage, it is called step-up transformer and when used to lower the voltage, it is called a step-down transformer. As in the case of nested coils discussed in the Pre-Lab Notes, the secondary coil has a varying magnetic field in its center due to the varying electric current (i.e., AC current) in the primary coil. The induced current and electric potential may be different in the secondary coil than in the primary coil. For N_P loops in the primary coil, N_S turns of the wire in the secondary, and a voltage supplied by the power source of V_P, the induced voltage in the secondary is given by

         (1) V S = N S N P V P

The induced current is

         (2) I S = N P N S I P

The second challenge is to find the ratio of the turns of the outer coil to the inner coil in the nested coil set. The constraint here is that you must use electromagnetic induction in your technique. Another minor limitation is that you don’t have access to the lab equipment. Two data sets are provided for you, You need to analyze them and come to conclusions.

The first data set is for a pair of nested coils, with the inner being the primary with an applied AC voltage at 60 Hz and the outer being the secondary. For the second data set, the primary and secondary roles are reversed.

Manufacturer specified Turns Ratio (TR) of outer coil to inner coil
TR	8.2
u{TR}	0.2
u(Vp) (V)	0.03
u(Vs) (V)	0.05
Inner	Outer
Vp (V)	Vs (V)
5.65	46.94
5.34	44.38
4.82	40.00
4.54	37.69
3.93	32.61
3.54	29.37
2.80	23.24
2.33	19.32
1.85	15.36
1.23	10.22
0.29	2.43
u(Vs) (V)	0.005
Outer	Inner
Vp (V)	Vs (V)
7.65	0.8793
6.85	0.7872
6.11	0.7019
5.59	0.6419
4.98	0.5719
4.18	0.4802
3.62	0.4163
2.88	0.3315
2.22	0.2628
1.67	0.1919
0.42	0.0485

Copy each of these data sets into Excel, graph them. And find the best fit. Upload the worksheet here.

Answer 1

As described in the question, the induced voltage in the secondary coil is given by,

Our aim is to find the ratio of the turns of the outer coil to the inner coil in the nested coil set. So if we plot the graph between primary voltage (Vp) and secondary voltage (Vs) from the data set for a pair of a nested coil and fit the linear line with zero intersect e.g. y = mx than the slope of the fitted line will give the value of the ratio of loops in secondary coil (Ns) and loops in primary coil (NP) and in terms of the nested coils where outer being the secondary and inner being the primary coil than the slope of the fitted line indicates the Turns Ratio (TR) for the nested coil.

The first data set for a pair of nested coils (where the inner coil being the primary coil and the outer being the secondary coil) are copied into the Excel sheet and plot the scatter plot in which primary voltage (VP) in the x-axis and secondary voltage (Vs) in the y-axis. The equation of a linear line with zero intersect (y=mx) is fitted (red line in the plot). The slope of the fitted line is 8.303 which gives the value of the ratio of loops in secondary coil (Ns) and loops in primary coil (NP) or Turn Ratio (TR) of the nested coil.

The screenshot of the worksheet with the graph is shown here:

For the second pair of nested coils, the role of the primary and secondary roles are reversed (where the inner coil being the secondary coil and the outer being the primary coil). The scatter plot in which primary voltage (VP) in the y-axis and secondary voltage (Vs) in the x-axis, is plotted. The equation of a linear line with zero intersect (y=mx) is fitted (red line in the plot). The slope of the fitted line is 8.697 which gives the value of the ratio of loops in primary coil (Np) and loops in secondary coil (Ns) or Turn Ratio (TR) of the nested coil.

The screenshot of the worksheet with the graph is shown here: