Download UNIT-1 Electric Circuit

Electrical Engineering & Control Systems (15EE232)
Ravi Chaurasia
Ph. -09411826365
[email protected]
Notes of lessons
UNIT-I
ELECTRIC CIRCUITS (DC CIRCUITS)
Ohm's law states that the current through a conductor between two points is
directly proportional to the potential difference across the two points. Introducing the constant of
proportionality, the resistance,[1] one arrives at the usual mathematical equation that describes
this relationship:
Where I is the current through the conductor in units of amperes, V is the potential difference
measured across the conductor in units of volts, and R is the resistance of the conductor in units
of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent
of the current.
Voltage Division
v1  R1i 
R1
v total
R1  R2  R3
v2  R2 i 
R2
v total
R1  R2  R3
Electrical Engineering & Control Systems (15EE232)
Ravi Chaurasia
Ph. -09411826365
[email protected]
Current Division Rule
i1 
R2
v

itotal
R1 R1  R2
i2 
R1
v

itotal
R2 R1  R2
KIRCHOFF’S LAW:
A German physicist Gustav Kirchhoff developed two laws enabling easier analysis of circuit
containing interconnected impedances. The first law deals with flow of current and is known as
Kirchhoff ‘s Current Law (KCL) while the second one deals with voltage drop in a closed
circuit and is known as Kirchhoff ‘s Voltage Law (KVL).
KIRCHHOFF ‘S CURRENT LAW (KCL):
It states that in any electric network the algebraic sum of currents meeting at any node of circuit
is zero. This low is based on Conservation of charge.
n
 i (t )  0
j 1
j
KIRCHOFFS VOLTAGE LAW (KVL) :
It states that the algebraic sum of voltages in any closed path, in a network traveled in a single
direction is zero. This low is based on conservation of energy.
Electrical Engineering & Control Systems (15EE232)
Ravi Chaurasia
Ph. -09411826365
[email protected]
n
 v (t )  0
j 1
j
SUPERPOSITION THEOREM
Statement: In a linear bilateral network containing several sources, the current through or
voltage across any branch in the network equals the algebraic sum of the currents or voltage of
each individual source considered separately with all other sources replaced by resistance equal
to the internal resistances. Or
The response of a circuit to more than one source can be determined by analyzing the circuit’s
response to each source (alone) and then combining the results
Analyze Separately, then Combine Results
Electrical Engineering & Control Systems (15EE232)
Ravi Chaurasia
Ph. -09411826365
[email protected]
For deactivation of sources
Current source is zero – open circuit as I = 0 and solve iX
Voltage source is zero – short circuit as V= 0 and solve iXv
i X  i Xv  i Xc
THEVENINS THEOREM
Statement; The current flowing through a load resistance connected across any two terminals A
and B of linear bilateral network is given by V oc/R i+R L. Where Voc is open circuit voltage
RI is the internal resistance as viewed from the open terminals. Or
Any resistive circuit or network, no matter how complex, can be presented as a voltage source in
series with a source resistance
Electrical Engineering & Control Systems (15EE232)
Ravi Chaurasia
Ph. -09411826365
[email protected]
Thevenin Resistance (RTH) – the resistance measured across the output terminals with the load
removed
Steps 1-Determine the open-circuit voltage Vt = voc.
2-Zero the sources and find the Thévenins resistance Rt looking back into the terminals
3-The Thévenin equivalent consists of a voltage source Vt in series with Rt .
Thévenins Equivalent Circuits
Electrical Engineering & Control Systems (15EE232)
Ravi Chaurasia
Ph. -09411826365
[email protected]
NEELKANTH INSTITUTE OF TECHNOLOGY, MEERUT
Department of Electrical and Electronics Engineering
Lecture Notes – 10
NORTONS THEOREM
Statement -Any resistive circuit or network, no matter how complex, can be represented as a
current source in parallel with a source resistance
Nortons Theorem
Any resistive circuit or network, no matter how complex, can be presented as a current source in
parallel with a source resistance.Or
According to this theorem any two terminal active network containing voltage sources and
resistance when viewed from its output terminal is equivalent to a constant current source and an
internal resistance in parallel
Norton Current (IN) – the current through the shorted load terminals
Electrical Engineering & Control Systems (15EE232)
Ravi Chaurasia
Ph. -09411826365
[email protected]
For Calculating Isc or In
Norton Resistance (RN) – The resistance measured across the open load terminals (measured
and calculated exactly like RTH)
Norton-to-Thevenin and Thevenin-to-Norton Conversions
Electrical Engineering & Control Systems (15EE232)
Ravi Chaurasia
Ph. -09411826365
[email protected]
Steps -1. Determine the short-circuit current In = isc.
2. Use the equation Vt = Rt In to compute the remaining value.
3. The Norton equivalent consists of a current source In in parallel with Rt .
Electrical Engineering & Control Systems (15EE232)
Ravi Chaurasia
Ph. -09411826365
[email protected]
Maximum Power Transfer Theorem
A resistive load withdraws maximum power from the circuit when the value of load resistance
equals the internal resistance of the network as viewed from the output terminals, with all energy
sources removed leaving behind the internal resistance. Or
The load resistance that absorbs the maximum power from a two-terminal circuit is equal to the
Thévenin resistance