Institute of Energy and Transport Systems

⇐ ПредыдущаяСтр 5 из 5

Peter the Great St.Petersburg Polytechnic University

The department of Theory of Electrical Engineering

The report on laboratory work №10

«Invesigation of the mutual inductance round

and square coils»

Students: 33212/1

Verhovcev D.

Ganzha I.

Nesgovorova E.

The lecturer: Kalimov A.G.

Saint Petersburg

1. Objective: Experimental and theoretical investigations of dependencies mutual inductance M round and square coils of the distance between them, as well as building on the basis of experimental data picture of the magnetic field of round coils.

2. Installation diagram

Round and square coils have 1000 and 500 winds.

R₁ = 32 mm; R₂ = 38 mm; l = 30 mm;

a = 130 mm; b = 130 mm; D = 10 mm; l = 25 mm;

3. Completing of the work. f=500 Hz.

Experiment №1. Two round coils

Round coil-round coil
Experiment	Dipole-wind	Wind- wind
x, m	U, V	I, А	ω =2π f	M, H	М, H	k^2	f(k)	M, H
0, 045		0, 098		0, 01300	0, 00146	0, 7076	0, 26	0, 0114
0, 05	3, 5	0, 098		0, 01137	0, 00118	0, 6622	0, 22	0, 0097
0, 06	2, 43	0, 098		0, 00790	0, 00082	0, 5765	0, 17	0, 0075
0, 07	1, 71	0, 098		0, 00556	0, 00060	0, 5000	0, 13	0, 0057
0, 08	1, 23	0, 098		0, 00400	0, 00046	0, 4336	0, 08	0, 0035
0, 09	0, 96	0, 098		0, 00312	0, 00037	0, 3769	0, 06	0, 0026
0, 1	0, 74	0, 098		0, 00240	0, 00030	0, 3289	0, 05	0, 0022
0, 11	0, 56	0, 098		0, 00182	0, 00024	0, 2882	0, 04	0, 0018
0, 12	0, 45	0, 098		0, 00146	0, 00021	0, 2539	0, 035	0, 0015
0, 13	0, 36	0, 098		0, 00117	0, 00018	0, 2248	0, 03	0, 0013
0, 14	0, 3	0, 098		0, 00097	0, 00015	0, 2000	0, 025	0, 0011
0, 15	0, 249	0, 098		0, 00081	0, 00013	0, 1788	0, 02	0, 0009
0, 16	0, 207	0, 098		0, 00067	0, 00012	0, 1607	0, 015	0, 0007
0, 175	0, 165	0, 098		0, 00054	0, 00010	0, 1379	0, 01	0, 0004
0, 19	0, 129	0, 098		0, 00042	0, 00008	0, 1195	0, 008	0, 0004
0, 205	0, 105	0, 098		0, 00034	0, 00007	0, 1044	0, 006	0, 0003
0, 22	0, 087	0, 098		0, 00028	0, 00006	0, 0919	0, 005	0, 0002
0, 235	0, 072	0, 098		0, 00023	0, 00005	0, 0815	0, 0045	0, 0002
0, 25	0, 06	0, 1		0, 00019	0, 00005	0, 0727	0, 004	0, 0002
0, 265	0, 051	0, 1		0, 00016	0, 00004	0, 0652	0, 0035	0, 0002
0, 28	0, 042	0, 1		0, 00013	0, 00004	0, 0588	0, 003	0, 0001
0, 295	0, 036	0, 1		0, 00011	0, 00003	0, 0533	0, 0025	0, 0001
0, 31	0, 03	0, 1		0, 00010	0, 00003	0, 0485	0, 002	0, 0001

Depending on the mutual induction of experimental and theoretical distance calculated by different methods.

Experiment №2. Two square coils

Experiment	Dipole-wind	Wind-wind
x, m	U, V	I, А	ω =2π f	M, H	М, H	М11'=M33'	M31'=M13'	M22'=M44'	M24'=M42'	М, Гн
0, 045		0, 18		0, 00708	0, 00127	5, 57E-08	-5, 42E-08	7, 46E-10	-2, 46E-10	9, 87E-04
0, 05	3, 45	0, 18		0, 00610	0, 00103	5, 18E-08	-5, 07E-08	6, 72E-10	-2, 43E-10	7, 96E-04
0, 06	2, 6	0, 18		0, 00460	0, 00072	4, 56E-08	-4, 48E-08	5, 61E-10	-2, 36E-10	5, 44E-04
0, 07	1, 95	0, 18		0, 00345	0, 00053	4, 06E-08	-4, 01E-08	4, 82E-10	-2, 29E-10	3, 89E-04
0, 08	1, 54	0, 18		0, 00272	0, 00040	3, 66E-08	-3, 62E-08	4, 22E-10	-2, 21E-10	2, 89E-04
0, 09	1, 25	0, 18		0, 00221	0, 00032	3, 33E-08	-3, 30E-08	3, 75E-10	-2, 14E-10	2, 21E-04
0, 1	0, 99	0, 18		0, 00175	0, 00026	3, 05E-08	-3, 03E-08	3, 38E-10	-2, 06E-10	1, 73E-04
0, 11	0, 8	0, 18		0, 00142	0, 00021	2, 81E-08	-2, 79E-08	3, 07E-10	-1, 98E-10	1, 38E-04
0, 12	0, 66	0, 18		0, 00117	0, 00018	2, 61E-08	-2, 59E-08	2, 81E-10	-1, 91E-10	1, 12E-04
0, 13	0, 55	0, 18		0, 00097	0, 00015	2, 43E-08	-2, 42E-08	2, 60E-10	-1, 84E-10	9, 15E-05
0, 14	0, 46	0, 18		0, 00081	0, 00013	2, 27E-08	-2, 27E-08	2, 41E-10	-1, 77E-10	7, 60E-05
0, 15	0, 39	0, 18		0, 00069	0, 00011	2, 14E-08	-2, 13E-08	2, 25E-10	-1, 70E-10	6, 37E-05
0, 16	0, 34	0, 18		0, 00060	0, 00010	2, 01E-08	-2, 01E-08	2, 11E-10	-1, 64E-10	5, 40E-05
0, 175	0, 267	0, 18		0, 00047	0, 00008	1, 86E-08	-1, 85E-08	1, 93E-10	-1, 55E-10	4, 27E-05
0, 19	0, 216	0, 18		0, 00038	0, 00007	1, 72E-08	-1, 71E-08	1, 78E-10	-1, 47E-10	3, 43E-05
0, 205	0, 18	0, 18		0, 00032	0, 00006	1, 60E-08	-1, 60E-08	1, 65E-10	-1, 39E-10	2, 79E-05
0, 22	0, 147	0, 18		0, 00026	0, 00005	1, 50E-08	-1, 49E-08	1, 54E-10	-1, 32E-10	2, 31E-05
0, 235	0, 123	0, 18		0, 00022	0, 00005	1, 41E-08	1, 49E-08	1, 44E-10	-1, 26E-10	1, 92E-05
0, 25	0, 105	0, 18		0, 00019	0, 00004	1, 32E-08	-1, 32E-08	1, 35E-10	-1, 99E-10	1, 62E-05
0, 265	0, 09	0, 18		0, 00016	0, 00004	1, 25E-08	-1, 25E-08	1, 28E-10	-1, 15E-10	1, 38E-05
0, 28	0, 078	0, 18		0, 00014	0, 00003	1, 19E-08	-1, 19E-08	1, 21E-10	-1, 10E-10	1, 18E-05
0, 295	0, 069	0, 18		0, 00012	0, 00003	1, 13E-08	-1, 13E-08	1, 15E-10	-1, 05E-10	1, 02E-05
0, 31	0, 06	0, 18		0, 00011	0, 00003	1, 08E-08	-1, 07E-08	1, 09E-10	-1, 01E-10	8, 83E-06

Depending on the mutual induction of experimental and theoretical distance calculated by different methods.

Experiment №3. Square-round coils

Experiment	Dipole-wind	Wind-wind
x, m	U, V	I, А	ω =2π f	M, H	М, H	k'	k''	f(k')	f(k'')	M, Гн
0, 045	4, 4	0, 183		0, 007657	0, 001368	0, 723	0, 778	0, 38	0, 33	0, 002025
0, 05	3, 9	0, 183		0, 006787	0, 001108	0, 680	0, 71	0, 31	0, 25	0, 001640
0, 06	2, 9	0, 183		0, 005047	0, 000769	0, 596	0, 666	0, 22	0, 18	0, 001139
0, 07	2, 225	0, 183		0, 003872	0, 000565	0, 520	0, 522	0, 19	0, 11	0, 000837
0, 08	1, 75	0, 183		0, 003045	0, 000433	0, 454	0, 447	0, 14	0, 093	0, 000641
0, 09	1, 365	0, 183		0, 002375	0, 000342	0, 396	0, 413	0, 12	0, 08	0, 000506
0, 1	1, 065	0, 183		0, 001853	0, 000277	0, 347	0, 369	0, 09	0, 06	0, 000410
0, 11	0, 865	0, 183		0, 001505	0, 000229	0, 305	0, 321	0, 049	0, 31	0, 000339
0, 12	0, 715	0, 183		0, 001244	0, 000192	0, 270	0, 287	0, 046	0, 27	0, 000285
0, 13	0, 59	0, 183		0, 001027	0, 000164	0, 239	0, 258	0, 043	0, 25	0, 000243
0, 14	0, 48	0, 183		0, 000835	0, 000141	0, 213	0, 214	0, 039	0, 23	0, 000209
0, 15	0, 405	0, 183		0, 000705	0, 000123	0, 191	0, 198	0, 034	0, 2	0, 000262
0, 16	0, 345	0, 183		0, 0006	0, 000108	0, 172	0, 186	0, 029	0, 018	0, 000230
0, 175	0, 27	0, 183		0, 00047	0, 000090	0, 148	0, 157	0, 024	0, 015	0, 000193
0, 19	0, 22	0, 183		0, 000383	0, 000077	0, 128	0, 239	0, 019	0, 011	0, 000163
0, 205	0, 175	0, 183		0, 000305	0, 000066	0, 112	0, 12	0, 015	0, 009	0, 000140
0, 22	0, 148	0, 183		0, 000258	0, 000057	0, 099	0, 11	0, 013	0, 007	0, 000122
0, 235	0, 124	0, 183		0, 000216	0, 000050	0, 088	0, 1	0, 01	0, 006	0, 000107
0, 25	0, 105	0, 183		0, 000183	0, 000044	0, 078	0, 086	0, 009	0, 005	0, 000094
0, 265	0, 09	0, 184		0, 000156	0, 000039	0, 070	0, 078	0, 008	0, 0045	0, 000084
0, 28	0, 076	0, 184		0, 000132	0, 000035	0, 064	0, 07	0, 007	0, 004	0, 000075
0, 295	0, 066	0, 184		0, 000114	0, 000032	0, 058	0, 062	0, 0055	0, 003	0, 000068
0, 31	0, 06	0, 184		0, 000104	0, 000029	0, 052	0, 057	0, 004	0, 002	0, 000061

Depending on the mutual induction of experimental and theoretical distance calculated by different methods.

Experiment №5. Construction of the picture of the magnetic field.

I=100 mА, U=10 mV, n=10, Δ U=10 mV, f=500 Hz.

№	Δ U=10	2Δ U	3Δ U	4Δ U	5Δ U	6Δ U	7Δ U	8Δ U	9Δ U	10Δ U=100
	0, 096	0, 075	0, 064	0, 055	0, 05	0, 046	0, 043	0, 041	0, 037	0, 035
	0, 145	0, 114	0, 099	0, 088	0, 081	0, 074	0, 069	0, 066	0, 063	0, 062
	0, 188	0, 149	0, 129	0, 116	0, 106	0, 099	0, 094	0, 089	0, 085	0, 083
	0, 245	0, 194	0, 167	0, 15	0, 139	0, 128	0, 122	0, 118	0, 111	0, 105
	0, 298	0, 236	0, 204	0, 183	0, 168	0, 157	0, 146	0, 139	0, 133	0, 13

Conclusion: We have conducted the laboratory research of round and square coils at different distances «x» between them. The experiment was carried out for both round and for square coils. Measurement errors exist due to instrumental errors. We got a mutual inductance depending on the distance between the coils. It was found that there is measurement error due to the little distance between the coils, which can be determined by a discrepancy between experimental and calculated curves at small distances. During the last experiment we also got the picture of the magnetic field.

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