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Kirchhoff’s Laws Reminder: there will be a Quiz on Chapter 1 next Monday (Jan.23) Review Electric Circuit Voltage Current Ohm’s Law > i + _ Vs + R v _ A more complex circuit … R1 a R2 b R3 v1 c v2 d Objective: determine voltage and current in a circuit Kirchhoff’s Voltage Law Kirchhoff’s Current Law 1 Preliminaries Branch Node Loop Voltage drop / rise Voltage Drops & Rises Defined + 5V a b The following statements are true and equivalent ØThere is a 5 V voltage drop from a to b is a 5 V voltage rise from b to a is a -5 V voltage rise from a to b ØThere is a -5 V voltage drop from b to a ØThere ØThere • The first expression is the most common • In most cases, we will be concerned with voltage drops Kirchhoof’s Voltage Law (KVL) “The algebraic sum of all voltage drops around any closed loop is zero” M ∑v m =0 m=1 M : numberof voltages in theloop vm : mth voltage – Satisfied around all loops of a circuit – A statement about energy conservation 2 Kirchhoof’s Current Law (KCL) “The algebraic sum of currents entering a node is zero” N ∑i n =0 n =1 N : number of branches connected to the node i n : n th current enteringthe node – Satisfied at all nodes of a circuit – A statement about charge conservation – Applies to larger, closed region of a circuit (“supernodes ”) Kirchhoff’s Current Law a. i 2 b. i1 h. i12 i3 i10 .i i8 .i i5 Supernode c. i4 .d i11 . g i7 . i6 9 e f Application of Kirchhoff’s Laws . a 5V 2Ω 4Ω .b 8Ω _+ .c - 3V + .d 3