Chapter 3 Electric Current & DC SE

CHAPTER 5 : ELECTRIC CURRENT & DC CIRCUITS
( 7 HOURS )

Terminology :

1. Electric Conduction : Kekonduksian elektrik.
2. Drift velocity : Halaju hanyut.
3. Current density : Ketumpatan arus.
4. Resistor : Perintang.
5. Resistance : Rintangan.
6. Resistivity : Kerintangan.
7. Electromotive force (e.m.f) : Daya gerak elektrik
(d.g.e).
8. Internal resistance, r : Rintangan dalam.
9. Kirchhoff’s laws : Hukum-hukum Kirchhoff.
10. Closed loop : Gelung tertutup.
11. Potential divider : Pembahagi keupayaan.
12. Instrument : Peralatan.
13. Potentiometer : Meter keupayaan.
14. Shunt : Pemirau.

Introduction : JOTTING
SPACE
An electric current, I is the orderly flow of electrons in a conductor, which is induced
by an electrostatic field.

While they are moving, the electrons are carrying negative charge which implies
that an electric current in metals as a stream of electrons.

Electrical Conduction :

1. The electric current is equal to the ratio of the charge, dq flowing through a cross
section of a conductor within a small period of time, to the length dt of this period
of time.

I = dq …..(5.1)
dt

Note : If the magnitude and direction of the flow of electric current do not change
in time (known as Direct Current (DC)), then the electric current is called a
constant current and is expressed by the formula :

I= Q
t

Relation between current and time :

© Physics Teaching Courseware
| Chapter 5 | Electric Current & DC | page 1 / 20 |

2. Electric current is a basic physical quantity. It is also a scalar quantity. The SI unit© Physics Teaching Courseware
for electric current is Coulomb per second (Cs-1) or normally known as Ampere, A,
while the dimension, [A] is I.

3. Direction of current flow :
• The direction of current flow is opposite of that of electron flow.

V -e V -e

-e -e

-e -e

Flow of current Flow of electrons

4. Electrical conduction in metal :

• In metal, there are a lot of free electrons moving randomly. JOTTING
SPACE
• When a metal is connected to an electrical source, these electrons will
flow in one direction to produce a current.

• Metals are usually good conductors of electricity.

5. Drift Velocity of Charges in a Conductor :

• Without electric field, electrons in a conductor move randomly (chaotic motion)
within the crystal lattice (just like the motion of gas in a closed system).

© Physics Teaching Courseware

• The movement of electrons in electric field (caused by a potential difference)
is called the ‘drift of electron’.

| Chapter 5 | Electric Current & DC | page 2 / 20 |

• Electrons move in uniform motion and induce an electric current. The electrons
become accelerated in the short distances between the collisions with the ions
of the crystal lattice.

E L
vd
Current, I

Fe Area, A

© Mohd. Hazri @ kmph

• During the collisions, their velocities change as part of their electric energy JOTTING
is transmitted to the ions. Then the electrons are again accelerated and will SPACE
again slow down as the result of collisions.

• The velocity of the electrons reaches a permanent mean value vd known as
the ‘drift velocity’.

• The drift velocity is expressed as :

vd = I …..(5.2)
Ane

where : I = Current flow.
A = Cross sectional area.
e = elementary charge (magnitude of electron charge).
n = Number of charge per unit volume (measured in C m-3).

Note : Product of ne is known as ‘density of charge carrier’.

Note : The drift velocity is a vector quantity and has SI unit of meter per
second (ms-1).

| Chapter 5 | Electric Current & DC | page 3 / 20 |

Example :
A copper wire that has cross-sectional area 1.0x10-5 m2 carries a current of 2.00 A. If the
number of free electrons per unit volume of copper is 1029, estimate the drift velocity of free
electrons in copper.

Ohm’s Law & Resistivity :

1. When electrons are drifted across a conductor, collisions between these electrons
and the atoms in the conductor cause resistance to the flow of the current.

2. Resistor :
= A component in an electrical circuit that is present because of its electrical
resistance.

© Physics Teaching Courseware
JOTTING
SPACE

3. In a scheme, a resistor is presented in the following way :

4. Factors considered in building a resistor :

Resistance, R of a conductor itself depends on : © Physics Teaching Courseware
a) Types of material of the conductor.
b) Length, l of the conductor. …..(5.3)
c) Cross-sectional area, A of the conductor.

R∝ l
A

Or R = ρ l 
A

where ρ = constant called ‘resistivity’ and depends on the material of the
conductor.

| Chapter 5 | Electric Current & DC | page 4 / 20 |

5. The Ohm’s Law states that :
“At a given temperature, the current flowing through a conductor is directly
proportional to the potential difference between the ends of the conductor.”

V∝I

Or V = R I …..(5.4)

where R = constant called ‘resistance’

Resistance is a scalar quantity. The SI unit for resistance is VA-1 or normally
known as Ohm (Ω).

V (V) V (V)

0 I (A) 0 I (A) JOTTING
Figure 1 Figure 2 SPACE

Note : Ohmic conductors are conductors which obey Ohm’s law (Figure 1).
E.g. Pure metal.
Non- Ohmic conductors are conductors which do not obey Ohm’s law
(Figure 2). E.g. Junction diode.

6. Relationship between conductivity, σ and resistivity, ρ :

σ= 1 …..(5.5)
ρ

Variation of Resistance with Temperature :

1. The resistance in a circuit is due to the interactions between the moving electrons
and the ions of the crystal lattice.

2. The change in temperature will affect the rate of collision between these electrons
and the atoms in the conductor as well as the resistance to the flow of the current.

3. The change of resistance, ∆R is directly proportional to the change of temperature,
∆T as well as the original value of the resistance, Ro.

∆R ∝ Ro∆T

or ∆R = αRo∆T …..(5.6a)

or R = Ro[1 + α(T – To)] …..(5.6b)

where α = the temperature coefficient of increase in the resistance.

| Chapter 5 | Electric Current & DC | page 5 / 20 |

Since R = ρ l  , then equation (5.6b) also can be written in terms of resistivity as :
A

ρ l  = ρO  l  [1 + α(T – To)]
A  A 

or ρ = ρO [1 + α(T – To)] …..(5.7)

where ρ = final resistivity (respects to T).
ρo = initial resistivity (respects to To).

Example :

The resistance of the tungsten filament of a bulb is 190 Ω when the bulb is alight and 15 Ω
when it is switched off. Estimate the temperature of the filament when alight. The room
temperature is 30oC and the temperature coefficient of resistance of tungsten is 4.5x10-3
oC-1.

Electrical Energy & Power : JOTTING
SPACE
1. Electrical Energy :
• Electrical energy can be transformed into different types of energy, such as
heat, light or mechanical work.
• Consider a circuit which contains a battery of voltage V and a receiver (such as
a resistor) connected between points A and B as shown in the following figure :

V

© Physics Teaching Courseware

The work performed (equals to the energy used) :

WA→B = UA – UB
= q(VA – VB)
= qVAB

Since, q = It

then, we may write the formula for work as : …..(5.8a)
W = VIt

| Chapter 5 | Electric Current & DC | page 6 / 20 |

When we apply Ohm’s law :
V = IR

then, the work of current may be expressed as : …..(5.8b)
W = I2Rt

Or W = V 2t …..(5.8c)
R

• Electrical energy is a scalar quantity and has SI unit of Joule (J).

2. Electrical Power :

• Every electrical appliance is characterised by a specific power. The power, P
of electric current defines the amount of work performed by the current in time.
P = dW
dt

• The work of current : JOTTING
W = VIt SPACE

then, we may express the power of electric current as : …..(5.11a)
P = VI

When applying Ohm’s law : …..(5.11b)
V = IR

then, the power of electric current may be expressed as :

P = I2R

Or P = V 2 …..(5.12)
R

Note : V refers to the potential difference across the resistors.

• Electric power is a scalar quantity and has SI unit of Js-1 or normally known as
Watt (W).

Example :

A filament bulb A is rated 240 V, 100 W and another bulb B is rated 240 V, 60 W.
(a) Find the ratio of the resistance of the filaments at their normal working temperature.
(b) If each of the bulbs are connected in turns to a 120 V supply, what is the power
dissipated from each bulb?

| Chapter 5 | Electric Current & DC | page 7 / 20 |

Direct Current, DC : JOTTING
1. Direct current refers to electric current which has constant magnitude as well as SPACE

direction of current flow.
2. Current flows from a point of higher potential to another point of lower potential.

This potential difference (also known as voltage) must be remained using a source
(or device) so that the flow of current is continuity.

Electromotive Force (e.m.f.), Internal Resistance & Potential Difference :
1. Electromotive force (e.m.f.) :

• Electromotive force (e.m.f.) is the electrical energy that generated by a source
(such as battery @ dry cell, power supply etc) so that the charge can flow from
one terminal to another terminal of the source through any resistor.

ξ

+ r-

© Mohd. Hazri @ kmph

• The electromotive force (e.m.f) of a cell is defined as :
= The amount of energy that is converted in the cell from chemical to electrical
form per unit charge passing through the circuit.
ξ= W
q

© Physics Teaching Courseware

• The unit of electromotive force is volt (V) :
1V = 1JC-1

| Chapter 5 | Electric Current & DC | page 8 / 20 |

2. Internal resistance, r :

VV

Figure 1 Figure 2

• If the battery (cell) is not connected to the circuit (figure 1), we obtain that :
V=ξ

• Therefore, e.m.f. also can be defined as :
= Potential difference (voltage) of the cell terminal without flowing current.

• However, if the same battery (cell) is connected to the circuit (figure 2), we

obtain that:
V<ξ

• Reduction of the voltage is due to the so-called ‘internal resistance’, r JOTTING
(resistance of the cell itself) through a relationship : SPACE

ξ = Vcircuit + Vcell …..(5.13a)

or ξ = IR + Ir …..(5.13b)

Note : Since the same current flows in the circuit as well as in the cell
itself, then the above equations can also be written as :

ξ = I(R + r) …..(5.13c)

Note : The emf of a battery is constant but the internal resistance
increases with time as a result of chemical reaction.

| Chapter 5 | Electric Current & DC | page 9 / 20 |

Relationship Between
Electromative Force (e.m.f.) @ Voltage and The Flow of Current

(Zahidi, 2008)

The Flow of
Electric Current

refers to…

The Rate of Charges
Flow in a Circuit

associated with…

The Rate of Electrons reason… Charge possessed by
Flow in a Circuit Electron

in Certain Direction

depends on… reason… Same Direction due
to the Same Type of
Coulomb Force
to accelerate all the Electrons Charge

to Flow in the
Same Direction

depends on… reason… Based on Formula :
F = qE
Electric Field
generated in the Circuit reason… Based on Formula :
E=V/d
depends on…

Voltage
Supplied by the Cell
(Electromotive Force)

JOTTING
SPACE

| Chapter 5 | Electric Current & DC | page 10 / 20 |

Example :
A dry cell of e.m.f. 1.5 V is connected in series with a resistor. When a current of 3.0 A
flows from the cell, the potential difference across the cell is 0.42 V. What is the internal
resistance of the dry cell and the resistance of the circuit ?

Resistors in Series and Parallel Circuits :
1. Uses of resistor :

a. To control electric current (if the resistors are arranged in parallel).
b. To divide (distribute) voltage (if the resistors are arranged in series).
2. Resistors arranged in series :

V JOTTING
SPACE
© Physics Teaching Courseware

For resistors which are arranged in series, the net voltage supplied is formulated as
follow :

V = V1 + V2 + V3 + … + Vn

or IR = I1R1 + I2R2 + I3R3 + … + InRn …..(i)

However, the current which flows through to each resistor : …..(ii)
I = I1 = I2 = I3 = … = In

From equations (i) and (ii), we conclude that :

R = R1 + R2 + R3 + … + Rn …..(5.16)

Example :
If resistors of 2 Ω, 3 Ω and 5 Ω are connected in series, calculate the equivalent resistance.

| Chapter 5 | Electric Current & DC | page 11 / 20 |

3. Resistor arranged in parallel :

© Physics Teaching Courseware

For resistors which are arranged in parallel, the nett voltage supplied is formulated
as follow :

V = V1 = V2 = V3 = … = Vn

or IR = I1R1 = I2R2 = I3R3 = … = InRn …..(i)

However, the current which flows through to each resistor :
I = I1 + I2 + I3 + … + In

or  V  =  V1  +  V2  +  V3  + ... +  Vn  …..(ii) JOTTING
 R  R1 R2 R3 Rn SPACE

From equations (i) and (ii), we conclude that :

 1  =  1  +  1  +  1  + ... +  1  …..(5.17)
 R  R1 R2 R3 Rn

Example :
If four resistors of 2 Ω are connected in parallel, calculate the equivalent resistance.

| Chapter 5 | Electric Current & DC | page 12 / 20 |

Kirchhoff’s Laws :

1. These laws are used to solve problems where there are more than one cell in the
circuit and Ohm’s law is insufficient (Ohm’s law can only be used if there is only
one cell in the circuit).

2. Kirchhoff’s 1st law :
Kirchhoff’s 1st law considers the total currents that flow through a junction in a
circuit.

© Physics Teaching Courseware

It states that :
“The algebraic sum of the current at a junction of a circuit is zero, since electric
charges do not stay at a junction”.

∑I=0 …..(5.18) JOTTING
SPACE

By considering : ∑Iin → +ve
∑Iout → -ve

Then, the equation (5.18) can also be written as :
∑ ( ∑ )Iin + − Iout = 0
∑ ∑or
Iin = Iout

Kirchhoff’s 2nd law :
Kirchhoff’s 2nd law considers any closed loop in a circuit.

It states that :
“For a closed loop, the algebraic sum of the voltages drops is equal to the
algebraic sum of the e.m.f.s.”

∑ξ = ∑(IR) …..(5.19)

Voltage changes in DC circuits : → V = +ξ
a. Sources of e.m.f. : → V=-ξ
If the loop crosses the e.m.f. from - to + terminal
If the loop crosses the e.m.f. from + to - terminal → V = +IR
b. Resistances : → V = - IR
If the loop in the direction of the current
If the loop in the direction opposite to the current

| Chapter 5 | Electric Current & DC | page 13 / 20 |

The closed loop can even following clockwise or anticlockwise.

ξ1 ξ1

ξ2 OR ξ2 JOTTING
OR SPACE
ξ1 - ξ2 = (I1R1) – (I2R2) - ξ1 + ξ2 = - (I1R1) + (I2R2)

Steps Taken To Analyze a Circuit Using Kirchhoff ‘s Laws :
(Zahidi 2006)

1. Simplify the closed circuit.
2. Use the 1st Kirchhoff’s law :

- Choose any junction and label as A.

- Identify the currents whose join the junction and label as I1, I2, I3, …
- Predict the direction of each current (if not given in the diagram).

- Determine the current which flow into the junction, Iin as well as away from
the junction, Iout.

- Use the formula :

∑I=0

or + I1 + I2 + I3 + … = 0 …..(i)

3. Use the 2nd Kirchhoff’s law :
- Choose one of the circuit involved.

- Draw a closed loop within direction (even following clockwise or
anticlockwise).

- Concentrate every side of the circuit with respect to the loop :
Determine the number of cell and its direction :

∑ ξ = ± ε1 ± ε2 ± ε3 ± ...

Determine the number of resistor and its respective current flows :

∑ (IR) = ± I1R1 ± I2R2 ± I3R3 ± ...

- Use the formula : …..(ii)

∑ ξ = ∑ (IR)

or + ξ1 + ξ2 + … = + (I1R1) + (I2R2) + …

4. If the combination between equation (i) and (ii) does not enough to solve the
problem, then repeat step 3 for other involved circuit.

5. Use all equation derived to solved the problem using mathematical skills (normally
to get the value of current flows and their respective directions).

6. If the sign of current is negative (in the answer), it means that the actual direction of
the current flow is in the opposite direction upon the predicted direction earlier.
However, the magnitude of the current remains the same.

| Chapter 5 | Electric Current & DC | page 14 / 20 |

Electrical Measuring Instruments :

1. In a natural science, such as physics, it is usual to conduct many experiments. As
we begin our practical exercises in physics, we first need to become acquainted
with the working of some electrical devices.

2. Galvanometer : 3. Ammeter :
A galvanometer is a device used for the An ammeter is a device used for
measurement of very week electric currents. measuring the electric current, I.

© Physics Teaching Courseware © Physics Teaching Courseware

4. Voltmeter : 5. Ohmmeter :
A voltmeter is a device that is used for An ohmmeter is an electric or
measuring the potential difference across electronic device used for
the electric current conductors. measuring the resistance.

© Physics Teaching Courseware © Physics Teaching Courseware

| Chapter 5 | Electric Current & DC | page 15 / 20 |

6. Potential Divider :
A potential divider is an electric circuit designed if we need a lower voltage to be
supplied to a particular receiver.

V © Physics Teaching Courseware I © Physics Teaching Courseware
R1 R2
OR

L1

V

The voltage across R1 is given by : The voltage across L1 is given by :

V = (R R1 ) V =  ρ L1  I
ξ 1 +R A
2

Or V =  R1 ξ R1
+ R2
JOTTING
7. Potentiometer : SPACE
A potentiometer is an electric circuit designed for measuring the e.m.f. of a cell
without the need to absorb any current from it. The idea involves the
compensation of unknown voltage by adjusting the known voltage.

© Physics Teaching Courseware The jockey is adjusted until the
galvanometer indicates zero
current. Point X is called ‘balance-
point’.

L Thus, the e.m.f. for cell X is given
X LX
by :

ξX = LX
ξ L

Or ξX = ξ LX 
L

The potentiometer has a better accuracy then a voltmeter because the reading is
measured from 0 to 100cm. A large scale gives a more accurate reading.

Note : In a disconnected circuit (or in balanced) : A B

ξR
A

Ammeter
V

Voltmeter

- Current does not flow in the circuit (I = 0) → showed by the ammeter.

- Resistor has no function.
- Potential difference between AB, VAB = ε → showed by the voltmeter.

| Chapter 5 | Electric Current & DC | page 16 / 20 |

Example 1

I1 ε1 r1 Since IG = 0 :

A VAP B R1 VA = VX
P
VP = VY
∴ VAP = VXY

..Basic concept of potentiometer.

G I=0 Circuit 1 :
ε1 = VAP + VPB + VR1 + Vr1
I2 Y or ε1 = I1 (RAP + RPB + R1 + r1)
X
…..(i)
ε2 r2
R2

Vxy VAP = I1RAP
…..(ii)

(i)÷(ii) ε1 = I1(R AP + RPB + R1 + r1 )
VAP I1(R AP )

∴ ε1 = R AP + RPB + R1 + r1 JOTTING
VAP R AP SPACE

…..(A)

Circuit 2 :
Since IG = 0 (circuit balanced) :

I2 = Ir2 = IR2 = 0

∴ ε2 = VXY
…..(B)

Combination (A) and (B) :

ε1 = R AP + RPB + R1 + r1 ; due to VXY = VAP
ε2 R AP ; due to RAP + RPB = RAB

or ε1 = R AB + R1 + r1
ε2 R AP

| Chapter 5 | Electric Current & DC | page 17 / 20 |

Example 2

I1 ε1 r1 Since IG = 0 :
VA = VX
A VAP B R1 VP = VY
P
∴ VAP = VXY = VR3
G I=0
Circuit 1 :
I2 Y ε1 = VAP + VPB + VR1 + Vr1
X or ε1 = I1 (RAP + RPB + R1 + r1)
R2 …..(i)
ε2 r2
R3 VAP = I1RAP
…..(ii)

VR3 (i)÷(ii) ε1 = I1(R AP + RPB + R1 + r1 )
VAP I1(R AP )

equivalents ∴ ε1 = R AP + RPB + R1 + r1
VAP R AP
JOTTING
…..(A) SPACE

I1 ε1 r1 Circuit 2 :
Even though IG = 0 (circuit
balanced) : P B R1
The circuit is connected.
VAP ε2 = Vr2 + VR2 + VR3
A ∴ ε2 = I2 (r1 + R2 + R3)
…..(iii)

X G I=0 Y VR3 = I2R3
I2 R3 …..(iv)

VR3 (iii)÷(iv) ε2 = I2 (r2 + R 2 + R3 )
VR3 I2 (R3 )
ε2 r2 R2

∴ ε2 = r2 + R2 + R3
VR3 R 3
…..(B)

Combination (A) and (B) :

ε1 = R3  R AP + RPB + R1 + r1  ; due to VAP = VR3
ε2 R AP r2 + R2 + R3

or ε1 = R3  R AB + R1 + r1  ; due to RAP + RPB = RAB
ε2 R AP r2 + R2 + R3

| Chapter 5 | Electric Current & DC | page 18 / 20 |

8. Wheatstone Bridge :
A Wheatstone bridge is an electric circuit designed for measuring the resistance
by comparing it with a model resistance.

© Physics Teaching Courseware Rx I1 I1 R

equivalents I1 G I1
b
a JOTTING
SPACE

© Physics Teaching Courseware

The jockey is adjusted until the galvanometer indicates zero current. Point D is
the ‘balance-point’.

Then, Va = VX …..(i)
Vb = VR …..(ii)

Besides, VX = I1RX …..(iii)
Va = I2Ra …..(iv)

Substitute equations (iii) and (iv) into (i) : …..(a)
I1RX = I2Ra

Besides, VR = I1R …..(v)
Vb = I2Rb …..(vi)

Substitute equations (v) and (vi) into (i) : …..(b)
I1R = I2Rb

Divide equation (a) to (b), thus the resistance of unknown resistor X is given by :

R X = Ra …..(5.20a)
R Rb

Since R = ρ L , then : R X = a …..(5.20b)
A Rb

| Chapter 5 | Electric Current & DC | page 19 / 20 |

Shunt and Multiplier :

1. The voltmeter and ammeter are sensitive devices. A small voltage or current
respectively will give an obvious deflection of the pointer. High current may burn
the wiring system of the moving-coil inside the devices.

2. Shunt :

max max

© Physics Teaching Courseware

The maximum reading for ammeter is called ‘full scale deflection’, IA (or Ifsd).
Ammeter has fixed resistance, rA (or rm).
If the same ammeter needs to be used to measure current of Imax which is
greater than IA, then we have to use the so-called ‘shunt’. A resistor of low
resistance, RS is connected in parallel to the ammeter to divert part of the
current, Is.

Thus, VS = VA JOTTING
Or SPACE
ISRs = IArA ; Is = Imax - IA
Or
IArA
Imax − IA
( )RS =

3. Multiplier :

IP

max

© Physics Teaching Courseware

The maximum reading for voltmeter is also called ‘full scale deflection’, Vm.
Voltmeter also has fixed resistance, rV.
If the same voltmeter needs to be used to measure voltage of Vmax which is
greater than Vm, then we have to use the so-called ‘multiplier’. A high
resistance resister RP is connected in series to the ammeter to reduce the
voltage across the voltmeter.

Thus, IP = IV
Or
( )IP =VP
Or RP

RP = Vmax − IV rV
IV

| Chapter 5 | Electric Current & DC | page 20 / 20 |