CHAPTER VII

DIRECT CURRENT CIRCUITS

A. DEFINITION OF ELECTRIC CURRENT

Electric current illustrated as a motion of positive charges

passing through from the higher potential to the lower

potential.

Electric current (i) defined as the amount of charge

passing through in every unit of time ( second ).

t

qi

e

qn n = the amount of electron

e = the electron charge/the elementary charge

= 1,6 x 10 -19 C

i = Electric current ( ampere )

q = charge ( coulomb )

t = unit of time ( second )

Direct current

source

Direction of electric

current

Direction of moving

electrons

B. RESISTANCE OF CONDUCTING WIRE

The resistance of a conducting wire depends on :

Length of the wire

Cross section Area

Kind of the wire

Temperature

Formula :

R = Resistance ( Ohm, Ω )

ρ = Resistivity of the material ( Ω m)

A = Cross-section Area ( m2)

L = Length (m)ΑR

ρ

MATERIALSRESISTIVITY

ρ(Ωm)

TEMPERATURE

COEFFICIENT(1/OC)

Silver

Copper

Gold

Aluminum

Tungsten

Iron

Platinum

Lead

Nichrome

Carbon

Germanium

Silicon

Glass

1,59 x 10-8

1,7 x 10-8

2,44 x 10-8

2,82 x 10-8

5,6 x 10-8

10 x 10-8

11 x 10-8

22 x 10-8

1,50 x 10-6

3,5 x 10-5

0,46

640

1010 - 1014

3,8 x 10-3

3,9 x 10-3

3,4 x 10-3

3,9 x 10-3

4,5 x 10-3

5,0 x 10-3

3,92 x 10-3

3,9 x 10-3

0,4 x 10-3

-0,5 x 10-3

-48 x 10-3

-75 x 10-3

Resistivities and TemperaturecCoefficients of Resistivity fo

various Materials

Temperature Influence for resistivity and

resistance

).1( TRR ot

If temperature of wire is increase, so the resistivity and the resistance of it is

increase

or TRR O ..

).1( Tot TO ..or

ρO = initial of resistivity (Ωm)

ρt = final of resistivity (Ωm)

Ro = initial of resistance(Ω)

Rt = final of resistance (Ω)

ΔT = the change of temperature (oC)

α = temperature coefficient of resistivity (/oC)

∆R = The change of resistance

∆ρ = The change of resistivity

C. OHM’S LAW

The ratio of the voltage (V) across a conductor to the

current (i) that flows through it is equal to a constant.

This constant is called resistance (R)

R = tan α

A = Ammeter

V = Voltmeter

L = Lamp

A

V

L

V

V

i

Graph of V - i

i = Current (A)

V = Voltage/the potential difference (V)

R = Resistance (Ω)

RiV Ri

V

MEASUREMENT OF CURRENT

AND VOLTAGE

D. SERIES AND PARALLEL CIRCUIT

Kirchhoff’s first rule:

The sum of the currents entering the any junction must equal the sum of the currents leaving the junction.

Example :

I1

i5i6

I2 i3

i4

i1 + i2 + i4 = i3 + i5 + i6

SERIES CIRCUIT (VOLTAGE DIVIDER)

i1 = i2 = i3 = I

RS = R1 + R2 + R3

V = V1 + V2 + V3

V1 : V2 : V3 = R1 : R2 : R3

Characteristic :

The current passing

through every resistor is

equal.

The potential difference

on every resistor is

different.

VR

RV

S

11 V

R

RV

S

22 V

R

RV

S

33

SRIV

V

R1 R2 R3

I

PARALLEL CIRCUIT (ELECTRIC CURRENT DIVIDER)

R3

1:

R2

1:

R1

1i:i:i

VV 3V 2V 1

3 R

1

2R

1

1R

1

R

1

iiii

321

P

321

Characteristics :

The current passing

through the junction is

different.

The potential difference

of every junction is

equal.

i3

R3

R1

R2

i1

i2i

V

IR

Ri

p

1

1I

R

Ri

p

3

3

pR

VI I

R

Ri

p

2

2

If in the galvanometer

(G) there are no electric

current passed, called a

galvanometer in

equilibrium condition

E. WHEAT STONE’S BRIDGE

Conducting wire

G

R2

LA LB

R1

R1 . RB = R2 . RAΑ

R

ρ

R1 . LB = R2 . LA

because

so;RA= wire resistance of part A

RB= wire resistance of part B

LA= wire length of part A

LB= wire length of part B

The forms of Wheat stone bridge:

R1 . R3 = R2 . R4

R1

R2

R3

R5R4

R4

R1 R2

R3

R5

R1 R2

R4

R5

R3

@

@

@

If:

so, R5 can be ignored

and then the wheat stone bridge circuit

can be simplified to:

R4

R1 R2

R3

R1 . R3 ≠ R2 . R4 Ifso, the circuits can be transforms to form Y (transformation of ∆ to

Y )

R4

R1R2

R3

R5

Ra

Rb

Rc

R2

R3

Ra

Rb

Rc

541

41aR

RRR

RR

541

51bR

RRR

RR

541

54cR

RRR

RR

F. SOURCE OF ELECTROMOTIVE FORCE (EMF)

Current in conductor is produced by an electric field, and

electric field is formed by the potential difference, devices

such as batteries and dynamos should be connected to the

circuit. These sources of electric energy are called source of electromotive force (ε)

ε

r

i

R

V

K

• When the switch K is open, the voltmeter reads is EMF (ε)

• When the switch K is closed, the voltmeter reads is clamping voltage (V)

V= i R V= clamping voltage = potential difference on the

external resistance

ε= EMF (volt)

r = internal resistance (Ω )

R = external resistance (Ω )

ε = i R + i r ε = i ( R + r )

If the batteries are identical, and

each has an EMF ε, and an

internal resistance r

Series Connection of Batteries

R

ε1 ε2 ε3

r1 r2 r3

Σε = n ε

Σr = n r

i

Σε = ε1 + ε2 +ε3

Σr = r1 + r2 + r3

r3

r1

r2

Parallel Connection of Batteriesε1

ε2

ε3

Σε = ε

For identical batteries:

i

R

Compound Connection of BatteriesE1

r1

E2

r2

E3

r3

E4

r4

E5

r5

E6

r1

E7

r2

E8

r3

E9

r4

E10

r5E11

r11

E12

r12

E13

r13

E14

r14

E15

r15

G. KIRCHHOFF’S SECOND RULES

or Σε = Σ (i. R)

Σ(i.R) = Dropping Potential difference

ε = EMF ( electromotive force )

Σε + Σ (i . R) = 0

The sum of the drops in potential difference in a close circuit is

equal to zero.

In applying Kirchhoff’s rules, the following rules should be noted:

1. Assign a symbol and direction to the currents in each part of the circuit

2. Loops are chosen and the direction around each loop is designated

3. The sign of the current are taken “+” when they are in the same direction of loops, and taken “-” when they are in the opposite direction of loops

4. The sign of the EMF are taken “+” when loops inside polar (+) of elements, and taken “-” when loops inside polar (-) of elements

G. WORK DONE BY THE ELECTRIC CURRENT ( JOULE’S LAW)

W = q V

W = electrical energy (J)

V = potential difference (volt)

q = charge (C)

i = electric current (A)

t = time ( s )

The amount of heat dissipated from a current carrying

conductor is proportional to the resistance of the

conductor, the square of current and the time needed

for the current to pass trough the conductor

Since q = i t, W = V i t

And V= I R W = i2 R t

R

V i

W = i2 R tR

V W

2

t

W P

P = Electric Power (Watt)

The electrical energy dissipated per unit time (second) is called electrical power.

t

ti V P i V P

t

Rti P

2

R2i P

t

tR

V

P

2

R

V P

2