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Chapter_26

# Chapter_26 - Chapter 26 Direct-Current Circuits Resistors...

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53 Chapter 26: Direct-Current Circuits Resistors in Series and Parallel (26-1) ± analysis of a circuit can often be simplified by replacing groups of resistors by a single resistor of equivalent resistance ± For resistors in series same current flows through each resistor 123 II I I === total voltage across set is sum of voltages across each to replace by single resistor, with equivalent resistance ± For resistors in parallel same voltage across each resistor ab VV V V == = total current through set is sum of currents through each to replace by single resistor, with equivalent resistance 1 R V b I 3 R 2 R I a b V a V x position () 11 2 2 33 1 2 3 ab V V I RI R I R I RR R =+ + + = + + eq ab VI R = eq 1 2 (series) R + " 3 12 111 ab I I V R V R + + ⎛⎞ + ⎜⎟ ⎝⎠ eq ab V I R = eq 1 2 (parallel) "reciprocal sum" 1 R + " 1 R V b I 3 R 2 R I a b V a V 1 I 2 I 3 I y position Path of least resistance carries most current 0 R ±²³ ²´ in wires

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54 ± example : find current I drawn from power supply (having negligible internal resistance) and voltage 2 V across 2 R equivalent resistance current drawn is voltage 2 V across 2 R is the same as across 1 R , which is the same as the voltage across a single equivalent resistor which is ± many practical resistor networks cannot be reduced to simple series-parallel combinations bridge circuit shown is one example use of Kirchhoff’s rules Kirchhoff’s Rules (26-2) ± junction : a point in a circuit where 3 or more conductors meet ± loop : any closed conducting path ± currents in arbitrarily complex circuit can be found from N linear equations in N unknowns using Kirchhoff’s two rules 1234 R E + 12 34 14V 3.0 k 6.0 k 2.0 k 6.0 k RR == Ω = Ω =Ω=Ω E ( ) ( ) 1234 1 2 3 4 (3)(6) (2)(6) k3 . 5 k 36 26 R R
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Chapter_26 - Chapter 26 Direct-Current Circuits Resistors...

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