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dc circuits 2 - Gustav Robert Kirchhoff(1824-1887 DC...

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1 1 DC Circuits - II Gustav Robert Kirchhoff (1824-1887) Last Time Resistors in series add Kirchhoff’s Laws: Loop law: conservation of energy Junction law: conservation of charge Resistors in parallel Examples Voltmeters and ammeters Today This lecture: HRW 27.7-27.8 For next time: HRW 27.9 2 Resistors in Parallel Resistors in parallel have the same potential across them. Use Kirchhoff’s Laws to find the equivalent resistance . Kirchhoff’s current law at node a, A. i 1 =i 2 +i 3 For the outer loop (clockwise), C. E -i 3 R 2 =0. For the left loop (clockwise), B. E -i 2 R 1 =0. Kirchhoff’s voltage law can be applied twice: We now have 3 equations, 3 unknowns: i 1 ,i 2 ,i 3 Note: we could have chosen the right loop instead of B or C . What about node b? 1 R 2 R E eq R 1 i 1 i 2 i 3 i a a b b -i 1 =-i 2 -i 3 , the same eq. 3 Resistors in Parallel (cont.) 1 = ; R 2 i E 2 = R 3 i E From B and C , 1 2 = + . R R 1 i E E Plug these into A , 1 2 1 1 = + R R 1 i E Rearranging, eq 1 2 1 1 1 = + R R R and since eq 1 = R 1 i E Ä For n parallel resistors,
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