Statement of Kirchhoff’s Rules

Junction Rule
• The sum of the currents entering any
junction must equal the sum of the
currents leaving that junction


A statement of Conservation of Charge
Loop Rule
• The sum of the potential differences
across all the elements around any
closed circuit loop must be zero

A statement of Conservation of Energy
Kirchoff’s Rules
(1) Node rule, current law,..
I2
I1 = I2 + I3
I1
=
I3
+
IR1
IR2
R1
R2
V
R3
I
V
V – IR1 – IR2 – IR3 = 0
V = I (R1 + R2 + R3)
= I Req
IR3
RECIPE
(1) Indicate currents going through each circuit elements:
* Realize that the same I flows through elements up to
the junction points.
* Make your best educated guess on the directions of I’s.
(2) The currents are your unknowns.
* You have to set up the same number of indep. Eqs.
* At least one of them come from the I-law and the rest of
them are from the V-law
(3) Set up the appropriate loops and apply V-law for each
loop. The direction of each loop can be either CW or CCW.
* If the loop runs from (-) to (+) of a battery, the battery
contributes (+) voltage (vice versa).
* If the loop runs in the same direction as that of your
current, the resistor contributes (-) voltage calculated
from Ohm’s Law (vice versa).
* Add all the contributions from the elements (R’s and
batteries) in the loop will be set to “0”. 1 equation.
++ After all, if you get (-) current value, that simply means
the current flows in the direction opposite to your guess.
I3
I1, I2, and I3
3 unknowns
5
6V
I2
3
I1
8V
I1 = I2 + I3
6 – 5*I2 – 8 = 0
2 + 5*I2 = 0
6 – 3*I3 = 0
I3 = 2 A
I1 = 1.6 A
I2 = - 0.4 A
This means that
Your guess on the
direction of I2 was
wrong and actual
current flows opposite
direction.
Does Ohm’s law say this?
• Ohm: A liquid measure formerly used in Germany, varying
locally between 30 and 36 gallons.
• With the same potential drop (voltage) applied, the larger
current flows through the smaller resistance.
• With the same current flowing, larger potential drop develops
across the larger resistance.
• If the resistance is infinite, no current flows regardless of
potential (voltage) difference across the resistor.
• When there is no potential difference across an element, no
current flows through regardless of the resistance.
Example 21.3
40
3V
50
4V
I1
10
5V
I2
20
I3
30
I2 = I1 + I3
4 – 40I1 – 3 – 10I1 – 20I2 = 0
4 – 50I3 – 5 – 30I3 – 20I2 = 0
1 – 50I1 – 20I2 = 0
-1 – 80I3 – 20I2 = 0
Electrical Safety



Electric shock can result in fatal burns
Electric shock can cause the muscles of
vital organs (such as the heart) to
malfunction
The degree of damage depends on
• the magnitude of the current
• the length of time it acts
• the part of the body through which it passes
Effects of Various Currents

5 mA or less
• can cause a sensation of shock
• generally little or no damage

10 mA
• hand muscles contract
• may be unable to let go a of live wire

100 mA
• if passes through the body for 1 second
or less, can be fatal
Ground Wire


Electrical
equipment
manufacturers use
electrical cords
that have a third
wire, called a
ground
Prevents shocks
Electrostatics and DC Circuit Revisited
Prof. Ohm
FIELD
E = F/q
F = qE
Hmm, they can
repel each other!
V = IR
R = V/I
I = V/R