1 Lecture 1 Dr Kelvin Tan Electrical Systems 100

2 Contents Resistance Ohm’s Law Series Circuits Parallel Circuits Voltage Divider Rule Current Divider Rule Kirchoff’s Voltage Law (KVL) Kirchoff’s Current Law

3 Resistance The flow of charge (q) in a material per unit time is current (i) I = dq/dt The resistance of a material is the property to resist the flow of electrons when an external electric field is applied. The resistance converts the applied energy into heat much like the mechanical friction due to colliding electrons and collisions between electrons and other atoms. The unit of Resistance is known as Ohms (  )

4 Resistance The Resistance of a material depends on its length (l), area (A) and the resistivity (  ) R =  l/A (  ) The Resistivity of some materials at 20 degree celsius. The unit is CM.  /ft and in SI system is Ohm-meters Resistivity (ρ) of various materials Silver9.9 Copper10.37 Gold14.7 Aluminium17.0 Tungsten33.0 Nickel47.0 Iron74.0 Nichrome295.0 Chlorite720.0 Carbon21,000.0

5 Resistance Resistors can be various types: Fixed Resistor Variable Resistors (Rheostat) Varistors Thermistors Photocells

6 Resistance Fixed and Variable Resistors The physical size (or shape) of a resistor is no clue to its resistance value, but can be a rough guide to its power rating.

7 Variable Resistors (Rheostat) - resistance change by turning a knob Resistance Thermistors - Resistance that varies rapidly and predictably with temperature A Varistor - Voltage Dependent Resistor or VDR Photocells - resistance change in light level

8 Color Coding of Resistors Example Find the resistance of a semiconductor resistance if the bands are: 1 st band is Gray, 2 nd band is Red, 3 rd band is Black, 4 th band is Gold, and fifth band is Brown? Solution: 82*(10e 0 ) (  ) ± 5% (1% reliability) 77.9  to 86.1  and 1out of every 100 will fail to satisfy manufacturer’s range after 1000 hr of operation.

9 Conductances Conductances are reciprocal of Resistances G = 1/R (siemens, S) or Mho G = A /  l (S or Mho)

10 A simple resistive circuit Electron flow direction Conventional current direction I I

11 Ohm’s Law Ohm’s Law states that the current through an electric path is dependant on the resistance of the path and is given by: + _ V I

12 V-I Characteristic of a Linear Resistor

13 Power SI unit is the Watt (I in Amperes, V in Volts and R in Ohms). 1 Watt is 1 Joules/Sec 1 hp = 746 Watts (the power of an average dray horse over a full working day) Electrical Power

14 Polarity references and the expression for power If the power is Negative (P <0), power supplied by circuit If the power is Positive (P > 0), power absorbed by the circuit + _ V I Absorb or supply ?

15 Energy: Electric Energy is the Electric Power consumed over a period of time SI unit is the Watt (I in Amperes, V in Volts and R in Ohms). 1 Watt is 1 Joules/Sec 1 hp = 746 Watts (the power of an average dray horse over a full working day) Electrical Energy How to calculate the Electric Power consumed in 1 day ?

16 The unit of Energy is Watt-hours (Wh), kWh, MWh or GWh Energy (Wh) = Power (W) * Time (h) 1 kWh is 1000 Wh 1 MWh = 1000 kWh 1 GWh = 1000 MWh We pay for electricity on the basis of kWh consumed in a specified 12 cents (approx) per kWh Electrical Energy How many kWh is this family using ??

17 Direct Current Circuits Analysis of simple circuits with batteries, resistors, and capacitors connected in various combinations (series/parallel). Kirchoff’s rules (based on law of conservation of energy and charge). Steady-state (current constant in magnitude and direction).

18 A simple resistive circuit

19 Circuit diagram V r = I × r V R = I × R I

20 The battery has an internal resistance r and is connected in series with a resistor R. Battery in Series with a Resistor Battery

21 Multiplying by the current yields: The total power of the battery is converted to heat in the two resistors. Battery in Series with a Resistor

22 Series connection of two resistors Req = R 1 + R 2

23 Two or more resistors are in series if connected together so that they have only one common point per pair. The current is the same through each resistor because any charge flowing through one resistor must also flow through the other. Two Resistors in Series

24 More than Two Resistors in Series The equivalent resistance of a series connection of resistors is always greater than any individual resistance.

25 Parallel connection of two resistors

26 Two Resistors in Parallel Two or more resistors are in parallel if there is an equal potential difference across each resistor. The current is not the same through each resistor because any charge flowing through one resistor cannot flow through the other. But the Potential difference (voltage) across each parallel branch is identical.

27 More than Two Resistors in Parallel The equivalent resistance of a parallel connection of resistors is always less than the smallest individual resistance.

28 Kirchoff’s Laws The sum of the currents entering any junction must equal the sum of the currents leaving that junction. (KCL) (Conservation of charge) The algebraic sum of the changes in potential across all of the elements around any closed circuit loop must be zero. (KVL) (Conservation of energy)

29 Kirchoff’s Voltage Law The algebraic sum of the changes in potential across all of the elements around any closed circuit loop must be zero. (KVL)

30 Kirchoff’s Voltage Law I V1V1 V2V2 K V L

31 Kirchoff’s Current Law Kirchoff’s Current Law states that the amount of current entering a junction must be equal to the current leaving that junction.

32 Kirchoff’s Current Law I1I1 I2I2 I3I3 Example : I 1 = 5A, I 2 = 2A and I 3 = 7A Taking current entering the node as reference I 1 +I 2 - I 3 = 0A Taking current leaving the node as reference I 3 -I 1 -I 2 = 0A

33 Kirchoff’s Current Law Example : I 1 =2A I 2 =3A I 3 =5A I 4 =1A I 5 = 6A a b Node (a) KCL I1 + I2 + I3 = 0 Node (b) KCL I3 + I4 + I5 = 0

34 Voltage Divider Rule In a Series Circuit, the Voltage across resistances divide according to the magnitude of the resistances Consider a Series circuit with two elements R 1 and R 2 and the total voltage applied across them is V. Let the current flowing through each of the two elements (series) be “I”

35 Voltage Divider Rule V + _

36 Current Divider Rule The current in parallel circuit elements divide in ratios according to the inverse of their resistor values. Consider two parallel elements R1 and R2 and a total current I, then the current in two elements are:

37 Current Divider Rule I I I1I1 I1I1 I2I2 I2I2

38 Single Subscript Voltage Notation Va means that the voltage of point “a” is Va with respect to the ground. VaVa VbVb

39 Double Subscript Voltage Notation Vab means that the voltage of point “a” with respect to point “b” is Vab V ab = V a – V b V ba = V b – V a = - V ab

40 If point “b” is at ground potential then V ab is simply V a Vab = Va – 0 = Va

41 What is V ab ?

42 Measurement of Voltage Voltages are measured by an instrument called Voltmeter. They can be either analog (AVO) or digital (DMM). Voltmeters are always connected in parallel with circuit where the voltage is to be measured. Voltmeters should have very high resistance, so that they do not allow current flowing through the circuit to enter in them due to their insertion.

43 Measurement of Voltage I + V R -

44 Measurement of Current Currents are measured by an instrument called Ammeter. An Ammeter can be analog or digital. An Ammeter is always connected in series with the circuit where current need to be measured. An Ammeter should have almost zero resistance, so that they do not alter the magnitude the of the current due to their insertion.

45 Measurement of Current I

46 An Open Circuit An Open circuit is one which have voltage across it but current through it is zero. An open circuit is represented by infinite resistance.

47 A Short Circuit A short circuit is one which allow current through it but voltage across it is zero. A short circuit is represented by zero resistance.