two-loop_circuit - 2 1 2 2 1 4 1 V V I R I R R 1 3 3 1 4 1...

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Two-loop Circuit Given: F i n d : 110 1 R ? 1 I 40 2 R ? 3 I 30 3 R 50 4 R V v 6 1 V v 8 2 The circuit in the figure is composed of two batteries ( E 1 = 6 V and E 2 = 8 V) and four resistors ( R 1 = 110 , R 2 = 40 , R 3 = 30 , and R 4 = 50 ) as shown. (a) What is the current I 1 which flows through R 1 ? (b) What is the current I 3 that flows through R 3 ? Solutions a.) To find I & we can use the following formula: 1 3 I We need to write three equations (two with voltage and one with currents)
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Using the red loop we get: 0 1 4 2 2 2 1 1 1 I R V I R I R V Using the purple loop we get: 0 0 1 4 3 3 1 1 1 I R I R I R V The current equation is: 3 2 1 I I I Let’s rewrite the equations:
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Unformatted text preview: 2 1 2 2 1 4 1 V V I R I R R 1 3 3 1 4 1 V I R I R R 3 2 1 I I I We are going to use Matrix to solve for the currents: 1 1 1 3 4 1 2 4 1 R R R R R R A 3 2 1 I I I B 1 2 1 V V V C C B A * C A B 1...
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This note was uploaded on 01/26/2012 for the course PHYSICS 211 taught by Professor Selig during the Fall '10 term at University of Illinois, Urbana Champaign.

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two-loop_circuit - 2 1 2 2 1 4 1 V V I R I R R 1 3 3 1 4 1...

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