Series Circuits
EE 2010: Fundamentals of Electric CircuitsMujahed AlDhaifallah
Is this a series circuit?
R1
R2
Is this a series circuit?
R1
R2R3
Is this a series circuit?
R1
R2R3
Series Circuit
Two elements are in series ifThey have only one terminal in common. The common point in the two elements is not
connected to a third current carrying element.
Resistance
Resistance is proportional to lengthlength
direction of current flow
Resistance
R = ρ L/A ρ is the resistivity of
the material (units?)
Resistance
What happens if two elements are connected back to back?
length
direction of current flow
length
direction of current flow
Resistance
R = ρ (L1+L2)/A
R = R1 + R2
The total resistance of a series circuit is the sum of all the resistances in the path
Resistance
The resistance seen by the source
R=R1+R2
The two circuits on the right are equivalent
R1
R2
R1+R2
Voltage Drop?
The current through each resistor is calculated by the Ohm’s law=V1/R1
Where V1 is the voltage across the resistor.
=V/RT
Where RT is the total resistance in the circuit.
V1 = VxR1/RT
Power?
Power dissipated in each resistorP1 = V1
2/R1
P1 = (V2/RT2)x R1
Total power = V2/RT = P1 + P2 + …
Voltage Sources in Series
Voltage sources can be connected in series to increase or decrease the total voltage applied to the system.
Net voltage is determined by summing the sources having the same polarity and subtracting the total of the sources having the opposite polarity.
Kirchhoff’s Voltage Law
The algebraic sum of the potential rises and drops around a closed loop is zero.
KVL
V + V1+V2 = 0 Can anyone prove
this mathematically?
R1
R2V
V1
V2
Voltage Divider Rule
In a series circuit the voltage across the resistive elements will divide as the magnitude of the resistors
Interchanging Series Elements Elements of a series circuit can be
interchanged without affecting the total resistance, current, or power to each element.
In the Figures below, resistors 2 and 3 are interchanged without affecting the total resistance
Ground Terminal
This is not a loop. Or is it?
Ground Terminal
This is not a loop. Or is it?
Ground terminal means that the two points are both connected to ground and are at a zero potential. So this is a loop.
Internal Resistances The ideal voltage source has no internal
resistance and an output voltage of V volts with no load or full load
Every practical voltage source (generator, battery, or laboratory supply) has some internal resistance. Voltage across the internal resistance lowers the
source output voltage when a load is connected. For any chosen interval of voltage or current, the
magnitude of the internal resistance is given by
Rint = VL / IL
Parallel Circuits
EE 2010: Fundamentals of Electric CircuitsMujahed AlDhaifallah
Are these resistors in Parallel?
Are these resistors in Parallel?
Are these resistors in Parallel?
Parallel Elements
Two Elements, branches or networks are in parallel if they have two points in common.
Resistance
Resistance is inversely proportional to the cross sectional area
direction of current flow
Resistance
Resistance is inversely proportional to the cross sectional area
direction of current flow
direction of current flow
Resistance
R = ρ L/(A1+A2) Solving in terms of R1
and R2 gives 1/R = 1/R1 + 1/R2
The total value of the resistance is always smaller than the smallest resistance
Resistance, etc.
The total resistance will decrease with each new added parallel branch
The voltage across each resistor is the same The total current is the sum of all the branches The total power dissipated is the sum of power
dissipated in all resistors.
Kirchhoff’s Current Law
KCL states that the algebraic sum of the currents entering and leaving a point or junction is zero.
i1+i2+i3+i4=0
i1
i2 i3 i4
Current Divider Rule
For parallel elements of different value the current will split with a ratio equal to the inverse of their resistor value