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Lecture 24. Chapter 18 Kirchhoff’s Rules RC Circuits. Monday 22 March 1999. Physics 112. The Physics 112 Help Session. Tuesdays 6:00 - 7:00 pm. CANCELLED!. Mondays 5:30 - 7:00 pm. NSC Room 118. Kirchhoff's Rules. Junction Rule. 1) The sum of the currents entering a junction - PowerPoint PPT Presentation
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Chapter 18Kirchhoff’s Rules
RC Circuits
1) The sum of the currents entering a junction must equal the sum of currents leaving a junction. (Conservation of Charge)
2) The sum of potential differences across all the elements on any closed loop in a circuit must be zero. (Conservation of Energy)
Junction Rule
Loop Rule
2
2
10
5
3I
I3
I2
I1 I
VThe Junction Rule says that
I = I1 + I2 + I3
2
2
10
5
3I
I3
I2
I1 I
VWe can use the loop rule multiple times:
V - 3 I - 10 I2 - 2I = 0 V - 3I - 2I3 - 2I = 0
V - 3 I - 5 I1 - 2I = 0
We now have a system of 4 equations and 4unknowns. We can therefore solve for eachof the 4 unknown currents.
V - 3 I - 10 I2 - 2I = 0 V - 3I - 2I3 - 2I = 0
V - 3 I - 5 I1 - 2I = 0I = I1 + I2 + I3
IV I
1 5
5
IV I
3 5
2I
V I2
5
10
Plug these three intothe current equation.
IV I V I V I
5
5
5
10
5
2
10I = 8V - 40 I
I = 0.16 V
Plug this back into the other 3 equations...
I1 = 0.04 V I2 = 0.02 V
I3 = 0.1 V
For Applying Kirchhoff’s Rules
A) assign a direction to the current in eachbranch of the circuit. Just GUESS!! If yourguess is incorrect, the current will come outas a negative number, but the magnitude willstill be correct!
B) when applying the loop rule, you mustchoose a consistent direction in which to proceed around the loop (either clockwise or counterclockwise, your choice, but stick to it).
1) When you encounter a resistor in the directionof the current, the voltage drop is V = - I R
2) When you encounter a resistor opposite thecurrent, the voltage drop is V = + I R
R2
I
R1 I1
I2 - I1R1
+I2R2
3) When you encounter an emf in the directionyou’re going around the loop, the voltage change is +V
4) When you encounter an emf opposite thethe direction you’re going, the voltage change is -V
- V1
+ V2
V1 V2
5) The junction rule can only be applied n-1times in a circuit with n junctions.
6) Each new equation you write must containa current that you haven’t yet used.
7) To solve a system of equations with kunknown quantities, you need k independentequations.
2
2
10
5
3I
I3
I2
I1 I
V
This circuit has two junction points. Therefore,we can only use the junction rule ONE time.
Find the currents in each branch of this circuit.
I0 I1
I26
1
18 V
12
12 V+
_
+
_
1
a
f
e
c
b
d
There are two junction points, so we can applythe junction rule ONCE.
I0 = I1 + I2
6
1
18 V
12
12 V+
_
+
_
1
a
f
e
c
b
d
How many possible loops are there?
b c d a e f c d a b e f c b
We have 3 unknowns, so we need 3 equationstotal. Therefore, we need use only 2 of the 3equations provided by the loop rule. (The junctionrule gave us 1 equation already!)
I0 6
1
18 V
12
12 V+
_
+
_
1
a
f
e
c
b
d
I1
I2
Let’s go around bcda first.
-(6) I1 + 18 V - (12) I0 = 0
(12) I0 + (6) I1 = 18 V
I0 6
1
18 V
12
12 V+
_
+
_
1
a
f
e
c
b
d
I1
I2
Let’s go around efcb second.
12 V - (1) I2 + (6) I1 - (1) I2 = 0
(2) I2 - (6) I1 = 12 V