Solutions_31 - PHY2061 R D Field Chapter 31 Solutions Problem 1 1 How much current passes through the 1 resistor in the circuit shown in the Figure

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PHY2061 R. D. Field Solutions Chapter 31 Page 1 of 6 Chapter 31 Solutions Problem 1: How much current passes through the 1 resistor in the circuit shown in the Figure ? Answer: 6I/11 Solution: Since the potential drop across each resistor is the same (i.e. parallel) we know that 3 3 2 2 1 1 R I R I R I = = and in addition I I I I = + + 3 2 1 . Hence, I R R R R I R I R R I R I = + + = + + 3 1 2 1 1 3 1 1 2 1 1 1 1 and solving for I 1 gives I I R R R R I I 11 6 3 1 2 1 1 1 3 1 2 1 1 = + + = + + = r r r A B r r r r r r r r R r cut Problem 2: Consider the infinite chain of resistors shown in the Figure . Calculate the effective resistance, R , ( in Ohms ) of the network between the terminals A and B given that each of the resistors has resistance r = 1 Ohm . 1 3 I I 1 I 2 I 3
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PHY2061 R. D. Field Solutions Chapter 31 Page 2 of 6 R 1 = 4 24 V I I 2 I 1 R 2 = 12 R 0 = 3 Answer: 0.7 Solution: We first cut the infinite chain at the point shown in the figure and replace the infinite chain to the right of the cut by its effective resistance R . We then combine the three resistors in series and then combine r and R+2r in parallel giving, r R r R 2 1 1 1 + + = , which implies that 0 2 2 2 2 = + r rR R and ( ) . 73 . 0 3 1 r r R = + = Problem 3: Consider the circuit consisting of an EMF and three resistors shown in the Figure . How much current flows through the 4 resistor ( in Amps )? Answer: 3 Solution: The original circuit is equivalent to a circuit with and EMF and one resistor with resistance R tot given by = + = + = 6 3 3 3 eff tot R R , where R eff = 3 from = + = 3 1 12 1 4 1 1 eff R .
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.

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Solutions_31 - PHY2061 R D Field Chapter 31 Solutions Problem 1 1 How much current passes through the 1 resistor in the circuit shown in the Figure

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