Download 1.3 Series DC Circuit, Kirchhoff Voltage Law

Chapter 1:
Introduction and DC Circuit
AZRALMUKMIN BIN AZMI
Chapter 1.3:
Series DC Circuit, Kirchhoff Voltage Law,
Voltage Divider Rule, Notation
AZRALMUKMIN BIN AZMI
Introduction



The battery has ability to cause charge to flow through the
circuit.
The +ve terminal attracts the electron through the wire at
the same rate.
If we consider the wire to be an ideal conductor, the
potential difference V across the resistor equal the applied
voltage of battery
Introduction (Cont…)

The current is limited only by resistor R.
The higher R, The less I
The lower R, The higher I

The direction of conventional current flow (Iconventional) is
opposite to that of electron flow (Ielectron)
Series Resistors

Two elements are in series if:
- they have only one terminal in common.
- the common point between the two element is not
connected to another current-carrying element.
Series Resistors (Cont…)

The total resistance of a series configuration is the sum of
the resistance level.

The more resistor we add in series, the greater the
resistance (no matter what their value)
Series Resistors (Cont…)

When series resistor have the same value:
RT = total value of resistor (Ω)
N = number of resistor in series
R = the value of resistance
Series Resistors (Cont…)

Find RT
Series Circuit

A circuit is any combination of elements that will result in
a continues flow of charge, or current, through the
configuration.

The direction of conventional current in a series dc circuit
is such that it leaved the +ve terminal of the supply and
return to the –ve terminal.
Series Circuit (Cont…)

The current is the same at every point in a series circuit.
I  I1  I 2  I 3  I N

Voltage in series circuit is the total voltage (VT) of each
element circuit.
VT  V1  V2  V3  VN
Series Circuit (Cont…)
E
IS 
RT

Since E is fixed, the magnitude of the source current will
be totally dependent on the magnitude of RT
Series Circuit (Cont…)
V1  I S R1
V2  I S R2
V3  I S R3
RT  R1  R2  R3
E
IS 
RT
Series Circuit (Cont…)

Find RT, IS, V1, V2 and V3
Series Circuit (Cont…)

Find R1, and E
Series Circuit (Cont…)

Voltage measurement
Series Circuit (Cont…)

Current measurement
Series Circuit (Cont…)

Power distribution
PE  I S E
PE  P1  P2  P3
2
V
PN  I SVN  I RN 
RN
2
S
Series Circuit (Cont…)

Find RT, IS, V1, V2, V3, PE, P1, P2 and P3
Series Circuit (Cont…)

Voltage source
Kirchhoff’s Law

Gustav Robert Kirchhoff

Introduced 2 laws:
- Kirchhoff Voltage Law (KVL)
- Kirchhoff Current Law (KCL)
Kirchhoff’s Voltage Law (KVL)

KVL states that the algebraic sum of the potential rises
and drops around a closed path (closed loop) is zero (0)
 Vloop  0
 E  V1  V2  0
E  V1  V2

The sum of voltage applied is equal to the sum of load
voltages
Kirchhoff’s Voltage Law (KVL) (Cont…)

Find unknown voltage:
Kirchhoff’s Voltage Law (KVL) (Cont…)

Find V1 and V2:
Kirchhoff’s Voltage Law (KVL) (Cont…)

Find V2, I2, R1 and R2:
Voltage Divider Rule

The voltage across series resistive elements will divide as
the magnitude of the resistance levels.
RN
VN 
xE
RT
R1
V1 
xE
R1  R2  R 3
Voltage Divider Rule (Cont…)

Find V1:

Find V1 and V3:
Voltage Divider Rule (Cont…)

Find V1:

Find V1 and V3:
Notation

Voltage source and ground
Notation (Cont…)

Replace the notation for a –ve dc supply with the standard
supply.
Notation (Cont…)

Double-subscript notation
- the double-subscript notation Vab specifies point a as the
higher potential. If this is not the case, a negative sign
must be associated with the magnitude of Vab.
The voltage Vab is the voltage at a point a with respect to
point b.
Vab  Va  Vb
Notation (Cont…)

Single-subscript notation
- the single-subscript notation Va specifies the voltage at
point a with respect to ground (0 V).
- if the voltage is less than 0 V, a –ve sign must be
associated with the magnitude of Va
Notation (Cont…)

Find Vab:

Find Va:
Notation (Cont…)

Find Vb, Vc and Vac:
Notation (Cont…)

Find Vab, Vcb and Vc: