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Electrical Circuit Analysis

Electrical Circuit Analysis
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2015-01-14 02:52
FunctionCoordinate GeometryGeometric Construction
This example demonstrates basic electrical circuit analysis involving linear equations and geometric constructions in the coordinate plane. Using GeoGebra commands such as Polygon, Midpoint, and Segment, a circuit model can be constructed and analyzed. Suitable for high school physics and mathematics courses.

GeoGebra Commands & Parameters

  1. Polygon(J_8, K_8, L_8, M_8) → poli1_5, j_5, k_5, l_5, m_5
  2. Midpoint(J_8, K_8) → N_4
  3. Midpoint(M_8, L_8) → O_4
  4. Polygon(J_{23}, K_{23}, L_{23}, M_{23}) → poli1_{20}, j_{20}, k_{20}, l_{20}, m_{20}
  5. Midpoint(K_{23}, J_{23}) → P_8
  6. Midpoint(L_{23}, M_{23}) → Q_8
  7. Polygon(U, B_1, C_1, D_1) → poli2, u, b_1, c_1, d_1
  8. Midpoint(D_1, C_1) → E_1
  9. Midpoint(U, B_1) → B_2
  10. Midpoint(U, B_2) → C_2
  11. Midpoint(B_2, B_1) → D_2
  12. Segment(C_2, D_2) → t
  13. Polygon(U_3, B_3, C_3, D_3) → poli2_1, u_1, b_2, c_2, d_2
  14. Midpoint(D_3, C_3) → E_2
  15. Midpoint(U_3, B_3) → B_4
  16. Midpoint(U_3, B_4) → C_4
  17. Midpoint(B_4, B_3) → D_4
  18. Segment(C_4, D_4) → t_1
  19. Polygon(U_1, B_6, C_6, D_6) → poli2_2, u_2, b_3, c_3, d_3
  20. Midpoint(D_6, C_6) → E_3
  21. Midpoint(U_1, B_6) → B_5
  22. Midpoint(U_1, B_5) → C_5
  23. Midpoint(B_5, B_6) → D_5
  24. Segment(C_5, D_5) → t_2
  25. Polygon(U_2, B_8, C_8, D_8) → poli2_3, u_3, b_4, c_4, d_4
  26. Midpoint(D_8, C_8) → E_4
  27. Midpoint(U_2, B_8) → B_7
  28. Midpoint(U_2, B_7) → C_7
  29. Midpoint(B_7, B_8) → D_7
  30. Segment(C_7, D_7) → t_3
  31. Polygon(U_4, B_{10}, C_{10}, D_{10}) → poli2_4, u_4, b_5, c_5, d_5
  32. Midpoint(D_{10}, C_{10}) → E_5
  33. Midpoint(U_4, B_{10}) → B_9
  34. Midpoint(U_4, B_9) → C_9
  35. Midpoint(B_9, B_{10}) → D_9
  36. Segment(C_9, D_9) → t_4
  37. Polygon(J_{24}, K_{24}, L_{24}, M_{24}) → poli1_6, j_6, k_6, l_6, m_6
  38. Midpoint(J_{24}, K_{24}) → N_5
  39. Midpoint(M_{24}, L_{24}) → O_5
  40. Polygon(J_{25}, K_{25}, L_{25}, M_{25}) → poli1_7, j_7, k_7, l_7, m_7
  41. Midpoint(J_{25}, K_{25}) → N_6
  42. Midpoint(M_{25}, L_{25}) → O_6
  43. Polygon(J_{26}, K_{26}, L_{26}, M_{26}) → poli1_8, j_8, k_8, l_8, m_8
  44. Midpoint(J_{26}, K_{26}) → N_7
  45. Midpoint(M_{26}, L_{26}) → O_7
  46. Polygon(J_{27}, K_{27}, L_{27}, M_{27}) → poli1_9, j_9, k_9, l_9, m_9
  47. Midpoint(J_{27}, K_{27}) → N_8
  48. Midpoint(M_{27}, L_{27}) → O_8
  49. Line(B, yAxis) → c
  50. Line(C, yAxis) → d
  51. Line(D, xAxis) → e
  52. Line(E, xAxis) → f
  53. Line(N, xAxis) → g
  54. Line(A, xAxis) → b
  55. Line(O, xAxis) → h
  56. Line(P, yAxis) → i
  57. Line(Q, yAxis) → j
  58. Intersect(h, yAxis) → T
  59. Intersect(h, c) → Z
  60. Segment(T, Z) → k
  61. Intersect(i, b) → A_1
  62. Intersect(i, k) → N_1
  63. Intersect(b, j) → O_1
  64. Intersect(j, xAxis) → P_1
  65. Intersect(yAxis, xAxis) → Q_1
  66. Intersect(c, xAxis) → Z_1
  67. Intersect(d, xAxis) → A_2
  68. Intersect(g, d) → N_2
  69. Segment(A_1, N_1) → l
  70. Segment(T, N_6) → m
  71. Segment(N_5, O_7) → q
  72. Segment(O_5, Z_1) → a_1
  73. Segment(O_8, A_2) → e_1
  74. Segment(Q_1, P_8) → f_1
  75. Segment(P_1, E_1) → h_1
  76. Segment(B_2, O_1) → i_1
  77. Intersect(q, g) → T_1
  78. Segment(T_1, N_2) → r
  79. Point(i_1) → O_2
  80. Point(h_1) → P_2
  81. Segment(Q_1, O_6) → p
  82. Segment(P_1, Q_8) → g_1
  83. Segment(N_8, N_2) → s
  84. Segment(N_7, Z) → n
  85. Segment(A_1, O_1) → j_1
  86. Polygon(J_{30}, K_{30}, L_{30}, M_{30}) → poli1_2, j_3, k_2, l_2, m_2
  87. Midpoint(K_{30}, J_{30}) → P_4
  88. Midpoint(L_{30}, M_{30}) → Q_3
  89. Polygon(J_{29}, K_{29}, L_{29}, M_{29}) → poli1_3, j_4, k_3, l_3, m_3
  90. Midpoint(K_{29}, J_{29}) → P_5
  91. Midpoint(L_{29}, M_{29}) → Q_4
  92. Polygon(J_{39}, K_{39}, L_{39}, M_{39}) → poli1_1, j_2, k_1, l_1, m_1
  93. Midpoint(J_{39}, K_{39}) → N_3
  94. Midpoint(M_{39}, L_{39}) → O_3
  95. Polygon(J_{40}, K_{40}, L_{40}, M_{40}) → poli1_4, j_{10}, k_4, l_4, m_4
  96. Midpoint(J_{40}, K_{40}) → N_9
  97. Midpoint(M_{40}, L_{40}) → O_9
  98. Polygon(J_{42}, K_{42}, L_{42}, M_{42}) → poli1_{10}, j_{11}, k_{10}, l_{10}, m_{10}
  99. Midpoint(J_{42}, K_{42}) → N_{10}
  100. Midpoint(M_{42}, L_{42}) → O_{10}
  101. Polygon(J_{41}, K_{41}, L_{41}, M_{41}) → poli1_{11}, j_{12}, k_{11}, l_{11}, m_{11}
  102. Midpoint(J_{41}, K_{41}) → N_{11}
  103. Midpoint(M_{41}, L_{41}) → O_{11}
  104. Line(Q_2, xAxis) → n_1
  105. Line(T_2, yAxis) → p_1
  106. Line(Z_2, yAxis) → q_1
  107. Line(A_3, yAxis) → r_1
  108. Line(P_3, xAxis) → s_1
  109. Line(R_3, xAxis) → a_2
  110. Line(S_3, yAxis) → e_2
  111. Intersect(yAxis, n_1) → T_3
  112. Intersect(e_2, n_1) → V_3
  113. Intersect(e_2, s_1) → W_3
  114. Intersect(s_1, r_1) → Z_3
  115. Intersect(s_1, p_1) → A_4
  116. Intersect(n_1, q_1) → F_4
  117. Intersect(q_1, a_2) → G_4
  118. Intersect(p_1, a_2) → H_4
  119. Intersect(xAxis, p_1) → I_4
  120. Intersect(a_2, r_1) → R_4
  121. Intersect(a_2, yAxis) → S_4
  122. Intersect(yAxis, xAxis) → T_4
  123. Segment(T_3, T_4) → g_2
  124. Segment(T_4, B_4) → h_2
  125. Segment(E_2, I_4) → i_2
  126. Segment(N_3, O_{10}) → n_2
  127. Segment(G_4, O_9) → q_2
  128. Segment(N_9, F_4) → r_2
  129. Segment(F_4, Q_3) → s_2
  130. Segment(V_3, W_3) → a_3
  131. Segment(Z_3, A_4) → e_3
  132. Segment(Z_3, N_{11}) → g_3
  133. Segment(O_{11}, R_4) → h_3
  134. Segment(R_4, S_4) → i_3
  135. Segment(I_4, O_3) → n_3
  136. Segment(H_4, G_4) → p_2
  137. Segment(N_{10}, A_4) → f_3
  138. Segment(P_4, T_3) → f_2
  139. Polygon(J_{43}, K_{43}, L_{43}, M_{43}) → poli1_{12}, j_{13}, k_{12}, l_{12}, m_{12}
  140. Midpoint(K_{43}, J_{43}) → P_6
  141. Midpoint(L_{43}, M_{43}) → Q_5
  142. Polygon(J_{44}, K_{44}, L_{44}, M_{44}) → poli1_{13}, j_{14}, k_{13}, l_{13}, m_{13}
  143. Midpoint(K_{44}, J_{44}) → P_7
  144. Midpoint(L_{44}, M_{44}) → Q_6
  145. Polygon(J_{45}, K_{45}, L_{45}, M_{45}) → poli1_{14}, j_{15}, k_{14}, l_{14}, m_{14}
  146. Midpoint(K_{45}, J_{45}) → P_9
  147. Midpoint(L_{45}, M_{45}) → Q_7
  148. Polygon(J_{46}, K_{46}, L_{46}, M_{46}) → poli1_{15}, j_{16}, k_{15}, l_{15}, m_{15}
  149. Midpoint(J_{46}, K_{46}) → N_{12}
  150. Midpoint(M_{46}, L_{46}) → O_{12}
  151. Polygon(J_{47}, K_{47}, L_{47}, M_{47}) → poli1_{16}, j_{17}, k_{16}, l_{16}, m_{16}
  152. Midpoint(J_{47}, K_{47}) → N_{13}
  153. Midpoint(M_{47}, L_{47}) → O_{13}
  154. Line(V_4, xAxis) → p_3
  155. Line(W_4, yAxis) → q_3
  156. Line(Z_4, yAxis) → r_3
  157. Line(A_5, xAxis) → s_3
  158. Intersect(yAxis, s_3) → G_5
  159. Intersect(yAxis, p_3) → H_5
  160. Intersect(xAxis, yAxis) → I_5
  161. Intersect(xAxis, q_3) → R_5
  162. Intersect(r_3, xAxis) → S_5
  163. Intersect(r_3, p_3) → T_5
  164. Intersect(q_3, s_3) → U_5
  165. Intersect(q_3, p_3) → V_5
  166. Segment(B_7, G_5) → a_4
  167. Segment(E_4, U_5) → e_4
  168. Segment(U_5, N_{12}) → f_4
  169. Segment(P_9, H_5) → g_4
  170. Segment(Q_7, P_7) → h_4
  171. Segment(Q_6, T_5) → i_4
  172. Segment(T_5, S_5) → n_4
  173. Segment(S_5, Q_5) → p_4
  174. Segment(O_{12}, R_5) → r_4
  175. Segment(I_5, O_4) → s_4
  176. Segment(N_4, G_5) → a_5
  177. Point(i_2) → F_5
  178. Point(h_2) → W_5
  179. Point(a_4) → Z_5
  180. Point(e_4) → A_6
  181. Segment(P_6, I_5) → q_4
  182. Point(a_4) → E_6
  183. Segment(G_5, E_6) → e_5
  184. Polygon(J_{48}, K_{48}, L_{48}, M_{48}) → poli1_{17}, j_{18}, k_{17}, l_{17}, m_{17}
  185. Midpoint(K_{48}, J_{48}) → P_{10}
  186. Midpoint(L_{48}, M_{48}) → Q_9
  187. Polygon(J_{49}, K_{49}, L_{49}, M_{49}) → poli1_{18}, j_{19}, k_{18}, l_{18}, m_{18}
  188. Midpoint(K_{49}, J_{49}) → P_{11}
  189. Midpoint(L_{49}, M_{49}) → Q_{10}
  190. Polygon(J_{50}, K_{50}, L_{50}, M_{50}) → poli1_{19}, j_{21}, k_{19}, l_{19}, m_{19}
  191. Midpoint(K_{50}, J_{50}) → P_{12}
  192. Midpoint(L_{50}, M_{50}) → Q_{11}
  193. Polygon(J_{51}, K_{51}, L_{51}, M_{51}) → poli1_{21}, j_{22}, k_{21}, l_{21}, m_{21}
  194. Midpoint(K_{51}, J_{51}) → P_{13}
  195. Midpoint(L_{51}, M_{51}) → Q_{12}
  196. Polygon(J_{52}, K_{52}, L_{52}, M_{52}) → poli1_{22}, j_{23}, k_{22}, l_{22}, m_{22}
  197. Midpoint(J_{52}, K_{52}) → N_{14}
  198. Midpoint(M_{52}, L_{52}) → O_{14}
  199. Line(F_6, yAxis) → f_5
  200. Line(G_6, yAxis) → g_5
  201. Line(H_6, yAxis) → h_5
  202. Line(I_6, xAxis) → i_8
  203. Line(R_6, xAxis) → n_5
  204. Line(S_6, xAxis) → p_5
  205. Line(T_6, xAxis) → q_5
  206. Line(U_6, xAxis) → r_5
  207. Intersect(i_8, f_5) → V_6
  208. Intersect(i_8, h_5) → W_6
  209. Segment(P_{13}, V_6) → s_5
  210. Segment(W_6, Q_{12}) → t_5
  211. Intersect(h_5, q_5) → Z_6
  212. Intersect(g_4, n_4) → A_7
  213. Intersect(p_5, g_5) → E_7
  214. Intersect(q_5, g_5) → F_7
  215. Point(h_5) → G_7
  216. Segment(G_7, W_6) → a_6
  217. Intersect(r_5, h_5) → H_7
  218. Segment(H_7, O_{14}) → b_6
  219. Segment(P_{10}, F_7) → d_6
  220. Intersect(f_5, n_5) → I_7
  221. Intersect(f_5, p_5) → R_7
  222. Segment(A_7, Q_{11}) → e_6
  223. Segment(P_{12}, I_7) → f_6
  224. Segment(E_7, Q_{10}) → g_6
  225. Segment(P_{11}, R_7) → h_6
  226. Segment(F_7, A_7) → i_6
  227. Segment(F_7, E_7) → n_6
  228. Intersect(n_5, yAxis) → T_7
  229. Intersect(yAxis, r_5) → U_7
  230. Segment(I_7, T_7) → p_6
  231. Segment(T_7, B_5) → q_6
  232. Segment(E_3, U_7) → r_6
  233. Segment(U_7, H_7) → s_6
  234. Segment(V_6, R_7) → t_6
  235. Intersect(g_5, r_5) → S_7
  236. Segment(S_7, E_7) → a_7
  237. Point(q_6) → V_7
  238. Point(r_6) → W_7
  239. Polygon(J_{53}, K_{53}, L_{53}, M_{53}) → poli1_{23}, j_{24}, k_{23}, l_{23}, m_{23}
  240. Midpoint(J_{53}, K_{53}) → N_{15}
  241. Midpoint(M_{53}, L_{53}) → O_{15}
  242. Polygon(J_{54}, K_{54}, L_{54}, M_{54}) → poli1_{24}, j_{25}, k_{24}, l_{24}, m_{24}
  243. Midpoint(J_{54}, K_{54}) → N_{16}
  244. Midpoint(M_{54}, L_{54}) → O_{16}
  245. Polygon(J_{55}, K_{55}, L_{55}, M_{55}) → poli1_{25}, j_{26}, k_{25}, l_{25}, m_{25}
  246. Midpoint(K_{55}, J_{55}) → P_{14}
  247. Midpoint(L_{55}, M_{55}) → Q_{13}
  248. Line(Z_7, xAxis) → b_7
  249. Line(A_8, xAxis) → c_7
  250. Line(E_8, yAxis) → d_7
  251. Line(F_8, yAxis) → e_7
  252. Line(G_8, yAxis) → f_7
  253. Intersect(d_7, b_7) → H_8
  254. Intersect(b_7, yAxis) → I_8
  255. Intersect(d_7, c_7) → R_8
  256. Intersect(c_7, e_7) → S_8
  257. Intersect(b_7, f_7) → T_8
  258. Intersect(c_7, f_7) → U_8
  259. Intersect(f_7, xAxis) → V_8
  260. Intersect(e_7, xAxis) → W_8
  261. Intersect(xAxis, yAxis) → Z_8
  262. Segment(E_5, V_8) → g_7
  263. Segment(V_8, O_{15}) → h_7
  264. Segment(N_{15}, T_8) → i_7
  265. Segment(T_8, Q_4) → n_7
  266. Segment(U_8, Q_{13}) → p_7
  267. Segment(P_5, I_8) → q_7
  268. Segment(I_8, N_{13}) → r_7
  269. Segment(O_{13}, Z_8) → s_7
  270. Segment(Z_8, B_9) → t_7
  271. Segment(S_8, N_{16}) → a_8
  272. Segment(O_{16}, W_8) → b_8
  273. Segment(P_{14}, R_8) → c_8
  274. Segment(R_8, H_8) → d_8
  275. Point(t_7) → A_9
  276. Point(g_7) → E_9
  277. Textfield(res1) → CI1
  278. Textfield(res2) → campoInserimento1
  279. Textfield(volt) → campoInserimento5
  280. Textfield(res3) → campoInserimento2
  281. Textfield(res4) → campoInserimento3
  282. Textfield(res5) → campoInserimento4
  283. Segment(Q_9, Z_6) → i_5
  284. Intersect(g_5, n_5) → R_1
  285. Point(n_5) → F_9
  286. Segment(G_9, F_7) → c_6
  287. Segment(G_9, F_9) → e_8
  288. OrthogonalLine(G_9, s_6) → f_8
  289. Line(P_{10}, xAxis) → g_8
  290. Line(Q_{10}, xAxis) → h_8
  291. Intersect(g_8, f_8) → H_9
  292. Intersect(h_8, f_8) → I_9
  293. Intersect(f_8, xAxis) → S_9
  294. Segment(G_9, F_7) → n_8
  295. Segment(F_7, E_7) → p_8
  296. Segment(E_7, S_7) → q_8

AI Drawing Prompt Reference

Draw an electrical circuit model with one series power source and four parallel resistors. Start by drawing a quadrilateral to represent the power source, then draw midpoints between the power source's vertices. Next, draw four parallel resistors, each consisting of two midpoints and two vertices. Finally, connect the power source and resistors to form the complete circuit model.
The prompt above was compiled from the original drawing commands and is for reference only.