soln6 - The Hong Kong Polytechnic University Department of...

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The Hong Kong Polytechnic University Department of Mechanical Engineering 2008/09 Semester 1 ME4204 Mechatronics Systems Assignment 1 Name: Student ID: 1. Find out the currents through R1 and R3 in the circuit of Fig. 1. Given the voltage sources of V 1 = 10V, V 2 = 9V, V 3 = 1V, R 1 = 5 , R 2 = 10 , R 3 = 5 , R 4 = 5 . (20 marks) Fig. 1 Solutions: The steps are as follows: 1. Assume clockwise mesh currents i 1 and i 2 . 2. Since the circuit of Fig. 1 has 2 meshes and 0 current source, it will yield 2 (i.e. 2 – 0) equations in the 2 unknowns i 1 and i 2 , as shown in Fig. 1a. i 2 i 1 Fig. 1a
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i 1 + v 1 - 3. From Fig. 1b, the mesh equation for mesh 1 is: + v 2 - Fig. 1b V 1 – R 1 i 1 – V 2 – R 2 (i 1 – i 2 ) = 0 (1) Fig. 1c R R ) 2 (i 1 -i 2 ) + V 2 – R 3 i 2 – V 3 – R 4 i 2 = 0 (2 + v 3 - + v 4 - - v 2 + From (1), we get 15i 1 – 10i 2 = 1 (3) From (2), we get -10i 1 + 20i 2 = 8 (4) 4. Solving the linear system of equations (3) and (4), we get: i 1 = 0.5A, i 2
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This note was uploaded on 01/16/2010 for the course ENG 91301 taught by Professor Lui during the Spring '08 term at Hong Kong Institute of Vocational Education.

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soln6 - The Hong Kong Polytechnic University Department of...

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