Chapter 17 Electric current 17.5 Series and parallel resistors ;Kirchhoff’s rules. 17.12 Kirchhoff’s rules in complex circuits current

Statement of Kirchhoff’s Rules 17.5 series and parallel resistors ;Kirchhoff’s rules Statement of Kirchhoff’s Rules Junction Rule ( I = 0) The sum of the currents entering any point must equal the sum of the currents leaving that junction A statement of Conservation of Charge I1 = I2 + I3

Loop Rule ( V = 0) The sum of the potential changes around any closed circuit loop must be zero You must go around the loop in one direction The sum of the measured will equal zero The voltage across a battery is taken to be positive (a voltage rise) if traversed from – to + and negative if traversed in the opposite direction. The voltage across a resistor is taken to be negative (a drop) if the loop is traversed in in the direction of the assigned current and positive if traversed in the opposite direction Vba = - IR Vba = IR

Example Example Calculate the current I flowing into the node (3+ I ) A = 2 A I = 2 -3 = -1 A The current flowing into the node is – 1 A which is the same as +1 A flowing out of the node Example Calculate the current I defined in the diagram I +2 A = - 4 A I = (- 4 – 2 ) A = - 6 A I is in the opposite direction I + I = 6 A I = ( 6 – 6 ) A = A

ε ε There are “two” ways to connect circuit elements. + - ε I V1 V3 V2 Series combination: Kirchhoff’s rules :The sum of the potential changes around any closed circuit must be zero Apply the Loop Rule The current is the same in resistors because any charge that flows through one resistor flows through the other but the potential differences across them are not the same ( a ) Rs + - V I ε ( b ) Figure 17- 10 (a) three resistors in series ( b) the equivalent resistance Rs leads to the same current I,

ε ε 2) Parallel combination I R1 I Rp I R3 R2 + - I3 I1 A B + - A B I2 V Rp + - I A B ε ( b ) Figure 17 .11 ( a ) three resistors in parallel . ( b ) the equivalent single resistance Rp produces the same current I

Example 17.10 (a ) find the equivalent resistance of the resistors in figure 17.10 a ( b ) the current I in each resistor Solved in the text book (a ) (b ) ( c )

Conceptoal question I 10  V 30  From the circuit with source voltage V and Total current I, which resistor will have the greatest voltage across it? The resistor with the largest resistance (30 ) Which resistor has the greatest current flow through it? Same for all because series circuit If we re-ordered the resistors, what if any of this would change? Nothing would change 10  20  V I 30  T.Norah Ali Almoneef

Example A) find the current in the circuit shown in the figure . B ) find the potential difference across each circuit element In the figure, we had a 3kΩ, 10 kΩ, and 5 kΩ resistor in series,

Example From the figure find ( a ) I ( total current ) , Rp ( total resistance ) ( b ) I 1 , I 2 , I 3

Example Four resistors are connected as shown in figure. Find the equivalent resistance between points a and c. 4 R. 3 R. 2.5 R. 0.4 R. Cannot determine from information given .

Conceptual questions I 10 V 30 From the circuit with source voltage V and Total current I, which resistor will have the greatest voltage across it? The resistor with the largest resistance (30 ) Which resistor has the greatest current flow through it? Same for all because series circuit If we re-ordered the resistors, what if any of this would change? Nothing would change 10 20 V I 30

Total resistance would increase Total current would decrease If we added a resistor in series with these, what would happen to the total resistance, total current, voltage across each resistor, and current through each resistor? Total resistance would increase Total current would decrease Voltage across each resistor would decrease (All voltage drops must still sum to total in series circuit; Kirchhoff’s law of voltages) Current through each resistor would be lower (total current decreased, but same through each one) I

Conceptual questions from the circuit with source voltage V and Total current I, which resistor will have the greatest voltage across it? All the same in parallel branches Which resistor has the greatest current flow through it? The “path of least resistance” (10) What else can you say about the current through each branch? They will sum to the total I (currents sum in parallel circuits; Kirchhoff’s law of current)

If we added a resistor in parallel with these, what would happen to the total resistance, total current, voltage across each resistor, and current through each resistor? Total resistance would decrease Total current would increase Voltage across each resistor would still be V Current through each resistor would be higher and would sum to new total

17.12 Kirchhoff’s rules in complex circuits Kirchhoff’s rules permit us to analyze any dc circuit .including circuits too complex Using the two rules (1) the sum of all the potential drops around any closed path in a circuit is equal to zero. (2) The current entering any point = The current leaving. Example 17.15 Find the current in the circuit shown in the figure Solved in the text book

Conceptual questions What is the current in branch P? A) 2 A B) 3 A C) 5 A D) 6 A E) 10 A 5 A 8 A 2 A P Junction 6 A S Answer: 4 The current entering the junction in red is 8 A, so the current leaving must also be 8 A. One exiting branch has 2 A, so the other branch (at P) must have 6 A.

Conceptual questions Which of the equations is valid for the circuit below? 2 V 2  6 V 4 V 3  1  I1 I3 I2 A) 2 – I1 – 2I2 = 0 B) 2 – 2I1 – 2I2 – 4I3 = 0 C) 2 – I1 – 4 – 2I2 = 0 D) I3 – 4 – 2I2 + 6 = 0 E) 2 – I1 – 3I3 – 6 = 0 Answer: 3

quiz ΔVab= 27V Calculate ΔVab ΔVab if one battery is reversed?

quiz Calculate the current in the circuit.

quiz Find the current I, r and ε. I = 3 A r =2 W e =-5 V

Quiz Calculate the currents I1, I2, and I3 in the three branches of the circuit in the figure. I1 = - 0.87 A. I2 = 2.6 A. I3 = 1.7 A.

summary Loop Rule Kirchhoff’s Rules Series combination: 1- Loop Rule 2- Series combination: Parallel combination

Home work 45,46,71