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