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EC
Polikar
Lecture 4
Kirchoff: The Man, The Law, The Field
Ohm: The law
The amount of current passing through a conductor is directly proportional to the
voltage across the conductor and inversely proportional to the resistance of the
conductor.
I 
V
V  IR
R
_
I
V
+
R
V: The voltage difference between two
locations, aka potential difference.
It is analogous to pressure.
I: The amount of current flowing
between these two points. It is
analogous to flow.
R: Resistance between the two points.
So how did Ohm come with this law…?
Power
A conductor’s resistance to electric current produces heat. The greater the current passing
through the conductor, the greater the heat. Also, the greater the resistance, the greater the
heat. A current of I amps passing through a resistance of R ohms for t seconds generates
an amount of heat equal to I 2 Rt joules (a joule is a unit of energy equal to 0.239 calorie).
E 
1
T
 iv
Energy is required to drive an electric current through a resistance. This energy is supplied
by the source of the current, such as a battery or an electric generator. The rate at which
energy is supplied to a device is called power, that is power is energy supplied per unit
time. Power is often measured in units called watts. The power P supplied by a current of
I amp passing through a resistance of R ohms is given by
2
P I R
V
2
R
 VI
Gustav Robert Kirchoff
Born: 12 March 1824 in Königsberg, Prussia (now Kaliningrad, Russia)
Died: 17 Oct 1887 in Berlin, Germany
Kirchoff’s Laws
 Two sets of rules define circuit analysis:
 Kirchoff ’s current laws
 Kirchoff ’s voltage laws
 KCL: The algebraic sum of all currents in any given node is zero
 KVL: The algebraic sum of all voltages in any given loop is zero
 What is a node?
 What is a loop?
 What is an algebraic sum…?
Assumptions & Definitions
 Wires: We connect the components to each other by wires.
 Wires, just like any other component in a circuit, has an internal
resistance. However, since this resistance is so small, it is usually ignored.
We will “model” the wire as a zero-resistance device, just like we model
the ideal current meter as a zero-resistance device.
 Nodes: A node is defined as the point where two or more
components are connected to each other. You must show care,
however, in locating and counting the nodes.
RC
How many nodes are there in this circuit?
vA
RD
+
RE
RF
RB
Definitions
 Loops: Any trace that starts and ends at the same point is a “closed loop”.
 A loop typically follows components, but it can, jump across “space”.
 We need to understand how to locate, identify and count loops.
How many loops are there in this circuit?
 Short / open circuit: A short circuit is
simply connection of wires with no
other components in between. Open circuit
is a lack of connection between two
nodes.
R1
v1
-
R2
+
+
va
-
R3
Can you identify short and open circuits ?
R4
R5
Kirchoff’s Current Law
(KCL)
 Algebraic sum of all currents at any given node must be zero.
 This is equivalent to saying sum of all currents entering a node (let’s call
these negative currents) and the sum of all current leaving a node (and
let’s call these positive currents), must be equal.
 In other words, no current (or no charge) may accumulate at a node.
Current must flow!
i1
For node A:
-i1+i2+i3=0  i1=i2+i3
How about other nodes?
_
V
A
i2
+
i7
i5
i3
i6
i4
B
i8
i10
i9
i11
Kirchoff’s Voltage Law
(KVL)
 The algebraic sum of all voltages in a loop must sum to zero!
 The law states that energy must be conserved.
 This is where things may get little tricky, since you must follow a
norm for defining polarities:
 You may follow this simple rule: A voltage source produces energy
(power), so there is an increase in potential energy when you move from
its – to + terminal.
 Resistors consume energy / dissipate power, so there is a potential drop
across the terminals of a resistor, equivalent to the value of the resistor
times the current passing through that resistor (by Ohm’s law).
R2
_
For the loop on the left: +V- I.R2 – I.R1 = 0, or
I
V
R1 V=I(R +R )
+
1
2
More on KVL
 A good practice is always to choose your current directions first, and then
follow all potential drops and rises. Do not be concerned about choosing
the right direction. If at the end you find out that the results for a current
is negative, that means you picked the polarity wrong.
i1
_
V
A
i2
+
i7
i5
i3
i6
i4
B
i8
i10
i9
i11
Open & Short Circuits
 Remember:
 No current passes through an open circuit, however, there can, and
usually is a potential difference (voltage) across the terminals of the open
circuit.
 The potential difference between two points on a short circuit is, be
definition, zero; however, there can, and usually is a nonzero current
flowing through a short circuit.
_
A
V
+
+
C
vCD iCD=0
B
-
E
D
vBE=0 iBE≠0
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