ele290 chapter 1

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BASIC ELECTRICAL ENGINEERING ELE290

1.0 CIRCUIT ANALYSISThis topic will cover two methods of circuit analysis which are:-

a) Kirchoffs Current Law (KCL)b) Kirchoffs Voltage law (KVL)

1.0.1) Kirchoffs Current Law (KCL)Kirchoffs current law states that the algebraic sum of the current at a node/junction in a

network at any instant of time is zero. KCL may be expressed mathematically as:-

Where ij represents current in thejth element and nis the number of elements connected to

the node k. This means that the algebraic sum of the currents meeting at a junction is zero. If

the current s entering the node are taken as positive, the currents leaving the node are

negatives, or vice versa. The KCL maybe thought of to be a consequence of the conservation

of electric charge-charge cannot be created nor destroyed but must be conserved.

Figure 1 Application of KCL

KCL equation for Fig. 1 above can be expressed as:-

By rearranging the equation, the equation for node k can be rewritten as:-

With KCL, it is obvious that elements in series carry the same current value.

I 1 I 3I 2

n

j

ji1

0

054321

iiiii

1i

2i

3i

4i

5i

52143 iiiii

21 ii

32 ii

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1.0.2) Kirchoffs Voltage Law (KVL)Kirchoffs voltage law states that at any instant of time the sum of voltages in a closed circuit

equals to zero. KVL may be expressed mathematically as:-

Where vj represents the individual voltage in thejth element around the closed circuit having

n elements.

If the voltage drop from the positive polarity to the negative polarity is assigned as positive

sign, then the voltage rise from the negative polarity to the positive polarity is assumed as

negative, or vice-versa.

KVL is a consequences of the fact that no energy is lost or created in an electric circuit. It is

our choice whether to apply KVL clock-wise or anti clock-wise. As we go round the loop, it isalso our choice to add the voltage drops ( and subtract voltage rise) or add the voltage rise

(and subtracts voltage drop). Both methods are correct.

However, usually going clock-wise is chosen and voltage drop in elements is set as negative

values; meaning that any voltage drop in the closed circuit is subtracted.

- V 3+

10 V 5 V

+ V 1-+ V 2-

KVL direction

Figure 2 Application of KVL

By applying KVL onto the closed loop in Fig. 2, the equation below is obtained:-

By rearranging the equation, the equation for the closed circuit can be rewritten as:-

With KVL, it is obvious that elements in parallel connection have the same voltage drop

across them.

n

j

jv1

0

0510 321 VVVVV

3215 VVVV

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V1

+

-

V3

+

-

V2

+

-

1.1)Series and Parallel connection:-1.1.1) Series Connection

For impedances that is connected in series, addition of the impedances can be calculated

by adding each of the impedance.

R1 R3R2

1.1.2) Parallel ConnectionFor impedances that is connected in parallel, addition of the impedances must becalculated by using parallel concept from right to left part of the circuit. Normal addition

cannot be used.

R1 R2

21 VV

32 VV

321 RRRRTOTAL

21

111

RRRTOTAL

21

211

RR

RR

RTOTAL

21

21

RRRRRTOTAL

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1.2)Current Divider RuleWhen a current has to be divided among various resistors connected in parallel, the current is

divided by using the current divider rule:-

I T

I 1 I 2

R 1 R 2

1.3)Voltage Divider RuleWhen a voltage has to be divided among various resistors connected in series, the voltage is

divided by using the voltage divider rule:-

V

-

+R 1

R 2

V 1

V 2

+

+

-

-

21 IIIT

TIRR

RI

21

1

2

TIRR

RI

21

2

1

21 VVV

VRR

RV

21

2

2

VRR

RV

21

1

1

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Tutorials

1. Determine the following values

a.

10

5

10

510V I1

I2

VR1+ -

b.

2

3

1

510V

I1VR1

+

-

c.

20

5

15 24

10020VI2I1

VR1+

-

d.

10k

2.2k

4.7k

50k

1k

12k

5VI2

I1VR1

+

-

ele290 chapter 1

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