Solving Series circuits How to Whiteboards

A Series Circuit has many voltages, but only one current Note that the total voltage drops add to source voltage 1  V1 V1 = IR = (3 A)(1 ) = 3 V 24 V V2 = IR = (3 A)(2 ) = 6 V 2  V2 A2 V3 = IR = (3 A)(5 ) = 15 V 5  V3 A3 How to solve series: 1. Find the total resistance (1  + 2  + 5  = 8 ) 2. Find the one current (I = V/R = (24 V)/(8 ) = 3 A - all the ammeters read 3 A) 3. Use V = IR to find voltages (voltage drops)

I A1 A2 R1 R2 R3 Analogy - ping pong balls - electrons All start moving at once/speed of impulse, speed of particles Resistance anywhere along the tube limits flow everywhere

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What is the Total resistance? 11  5  7  20.0 V R tot = R1 + R2 + R3 ... = 5  + 7  + 11  = 23  23 

What is the reading on both ammeters? (The one current) (answer with 3 SF) 5  7  11  A2 A1 20 V I = V/R = (20 V)/(23 ) = .8696 = .870 A .870 A

What do the voltmeters read? (3 SF) 11  5  7  20.0 V V = IR V1 = (5 )(.8696 A) = 4.35 V V2 = (18 )(.8696 A) = 15.7 V 4.35 V, 15.7 V

What do the voltmeters read? (3 SF) 11  9  5  35 V 13  3  R = 41 , I = .8537 A V = IR V1 = (5 )(.8537 A) = 4.27 V V2 = (20 )(.8537 A) = 17.1 V V3 = (13 )(.8537 A) = 11.1 V V3 4.27 V, 17.1 V, 11.1 V

What do the voltmeters read? (3 SF) 200  90  500  V3 110  120 V 130  R = 1030 , I = .1165 A V = IR V1 = (500 )(.1165 A) = 58.3 V V2 = (90 )(.1165 A) = 10.5 V V3 = (330 )(.1165 A) = 38.4 V 58.3 V, 10.5 V, 38.4 V

What is the value of the mystery resistor if V1 reads 3.17 V (3 SF) ???  5  7  20 V I = V/R = (3.17 V)/(5 )= .634 A Rtot = V/I = (20 V)/(.634 A) = 31.55  Rtot = 5  + 7  + ?? = 31.55  ?? = 19.5  19.5 

V3 A3