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Transcript
R4 R2 R1 R5 R3 R6 Figure 1: Configuration of resistors used in part (c). Electric and Magnetic Fields - Homework 5 Chris White ([email protected]) (a) Explain why a wire can only carry a current if it is part of an electrical circuit. (b) State Kirchoff’s laws for electrical circuits, and describe which physical principles underly them. (c) Consider the set of resistors shown in figure 1. Show that the effective resistance of this configuration is given by R2 R3 R4 R5 R6 R = R1 + + . R2 + R3 R4 R5 + R4 R6 + R5 R6 If current I is flowing through the circuit, what is the power dissipated by the resistor R2 ? (d) If all of the resistors in part (c) have resistance Ri = r, consider adding more parallel blocks, with 4, 5, 6 etc. resistors. If the largest parallel block has N resistors, show that the effective resistance is R=r N X 1 . n n=1 If I is the current flowing through the circuit, what is the power dissipated by the nth block of resistors?
