Transcript T. Elsarnagawy, mde 207, semester 311, rcc

Kirchoff’s
Voltage & current
laws
T. Elsarnagawy, mde 207, semester 311, rcc
Kirchhoff’s voltage law
T. Elsarnagawy, mde 207, semester 311, rcc
Kirchhoff’s voltage law
is generally stated as:
The sum of all the voltage drops around a single closed
path in a circuit is equal to the total source voltage in
that closed path.
KVL applies to all circuits, but you must apply it to
only one closed path. In a series circuit, this is (of
course) the entire circuit.
T. Elsarnagawy, mde 207, semester 311, rcc
Kirchhoff’s voltage law
R1
VS
12 V
680 W
R2
1.5 kW
R3
2.2 kW
Notice in this series example that the sum of the resistor
voltages is equal to the source voltage.
I1= 2.74 mA R1= 0.68 kW
I2= 2.74 mA R2= 1.50 kW
I3= 2.74 mA R3= 2.20 kW
IT= 2.74 mA RT= 4.38 kW
T. Elsarnagawy, mde 207, semester 311, rcc
V1= 1.86 V P1= 5.1 mW
V2= 4.11 V P2= 11.3 mW
V3= 6.03 V P3= 16.5 mW
VS= 12 V PT= 32.9 mW
T. Elsarnagawy, mde 207, semester 311, rcc
T. Elsarnagawy, mde 207, semester 311, rcc
VOLTAGE DIVIDER
T. Elsarnagawy, mde 207, semester 311, rcc
Two resistor voltage divider
• The two resistor voltage divider is used
often to supply a voltage different from
that of an available battery or power
supply.
• In application the output voltage depends
upon the resistance of the load it drives.
T. Elsarnagawy, mde 207, semester 311, rcc
Voltage divider rule
The voltage drop across any given resistor in a series
circuit is equal to the ratio of that resistor to the total
resistance, multiplied by source voltage.
VS
Assume R1 is twice the size of
R2. What is the voltage across
R1? 8 V
T. Elsarnagawy, mde 207, semester 311, rcc
12 V
R1
R2
R1
Voltage divider
15 kW
VS +
20 V
R2
10 kW
What is the voltage across R2?
Notice that 40% of
The total resistance is 25 kW.
the source voltage is
Applying the voltage divider formula:
across R2, which
 R2 
 10 kW 
represents 40% of
V2  VS    20 V 
 8V
 25 kW 
 RT 
the total resistance.
T. Elsarnagawy, mde 207, semester 311, rcc
Voltage divider
Voltage dividers can be set up for a variable output using
a potentiometer. In the circuit shown, the output voltage
is variable.
VS +
15 V
What is the largest output
voltage available? 5.0 V
T. Elsarnagawy, mde 207, semester 311, rcc
R1
20 kW
R2
10 kW
VOUT
where
is the parallel
resistance of R2 and
the load resistor RL.
T. Elsarnagawy, mde 207, semester 311, rcc
Power in Series Circuits
R1
470 W
Use the voltage divider rule to
find V1 and V2. Then find the
power in R1 and R2 and PT.
Applying the voltage
divider rule:
 470 W 
V1  20 V 
  11.75 V
 800 W 
 330 W 
V2  20 V 
  8.25 V
 800 W 
T. Elsarnagawy, mde 207, semester 311, rcc
R2
330 W
VS +
20 V
The power dissipated by each
P=V2/R
resistor is:
11.75 V 

P1 
 0.29 W
PT =
470 W 2
8.25 V 

0.5 W
P2 
 0.21 W
330 W
2
}
A
Circuit Ground
The term “ground” typically means a
common or reference point in the circuit.
VS +
12 V
Voltages that are given with respect to
ground are shown with a single subscript. For
example, VA means the voltage at point A with
respect to ground. VB means the voltage at point B
with respect to ground. VAB means the voltage
between points A and B.
R1
5.0 kW
B
R2
10 kW
C
What are VA, VB, and VAB for the circuit shown?
VA = 12 V VB = 8 V VAB = 4 V
T. Elsarnagawy, mde 207, semester 311, rcc
Kirchhoff’s current law
T. Elsarnagawy, mde 207, semester 311, rcc
Kirchhoff’s current law is generally stated as:
The sum of the currents entering a node is equal to the
sum of the currents leaving the node.
Notice in the previous example that the current from
the source is equal to the sum of the branch currents.
I1= 7.4 mA
I2= 3.3 mA
I3= 2.3 mA
IT= 13.0 mA
R1= 0.68 kW V1= 5.0 V P1= 36.8 mW
R2= 1.50 kW V2= 5.0 V P2= 16.7 mW
R3= 2.20 kW V3= 5.0 V P3= 11.4 mW
RT= 386 W VS= 5.0 V PT= 64.8 mW
T. Elsarnagawy, mde 207, semester 311, rcc
Special case for resistance
of two parallel resistors
R1
R2
The resistance of two parallel resistors can be found by
1
R

either: T 1 1

R1 R2
R1 R2
or RT 
R1  R2
What is the total resistance if R1 = 27 kW and
R2 = 56 kW? 18.2 kW
T. Elsarnagawy, mde 207, semester 311, rcc
Parallel current
sources
1.0 mA
1.5 mA
R
2.2 kW
Current sources in parallel can be combined algebraically
into a single equivalent source.
The two current sources shown are aiding, so the
net current in the resistor is their sum (2.5 mA).
(a) What is the current in R if the 1.5 mA source is
reversed? 0.5 mA
(b) Which end of R will be positive? The bottom
T. Elsarnagawy, mde 207, semester 311, rcc
T. Elsarnagawy, mde 207, semester 311, rcc
Current divider
When current enters a junction it divides with current
values that are inversely proportional to the resistance
values.
The most widely used formula for the current divider
is the two-resistor equation. For resistors R1 and R2,
 R2 
 R1 
I1  
 I T and I 2  
 IT
 R1  R2 
 R1  R2 
Notice the subscripts. The resistor in the numerator is
not the same as the one for which current is found.
T. Elsarnagawy, mde 207, semester 311, rcc
Power in parallel circuits
Power in each resistor can be calculated with any of the
standard power formulas. Most of the time, the voltage is
V2
known, so the equation P 
is most convenient.
R
As in the series case, the total power is the sum
of the powers dissipated in each resistor.
What is the total power if 10 V is applied to the parallel
combination of R1 = 270 W and R2 = 150 W? 1.04 W
T. Elsarnagawy, mde 207, semester 311, rcc
Key Terms
Branch One current path in a parallel circuit.
Current divider A parallel circuit in which the currents divide
inversely proportional to the parallel branch
resistances.
Junction A point at which two or more components are
connected. Also known as a node.
Kirchhoff’s A law stating the total current into a junction
current law equals the total current out of the junction.
Parallel The relationship in electric circuits in which
two or more current paths are connected
between two separate points (nodes).
T. Elsarnagawy, mde 207, semester 311, rcc
Key Terms
Circuit ground A method of grounding whereby the metal
chassis that houses the assembly or a large
conductive area on a printed circuit board is
used as a common or reference point; also
called chassis ground.
Kirchhoff’s A law stating that (1) the sum of the voltage
voltage law drops around a closed loop equals the source
voltage in that loop or (2) the algebraic sum of
all of the voltages (drops and source) is zero.
Open A circuit condition in which the current path is
broken.
T. Elsarnagawy, mde 207, semester 311, rcc