1 CHAPTER 2 EET 101 [Electric Circuit I]: V2009 School of Computer and Communication Engineering, UniMAP Prepared By: Prepared By: Wan Nur Suryani Firuz bt Wan Ariffin Amir Razif A. b. Jamil Abdullah Resistive Circuit

2 RESISTIVE CIRCUIT  Series/parallel resistor  Voltage divider circuit  Current divider circuit  Voltage and current measurement  Wheatstone bridge  Delta-wye (Pi-Tee) equivalent circuit

3 SERIES/PARALLEL RESISTOR  Resistors in series: Resistance equivalent R eq = R 1 + R 2 + ……….+ R N

4 Current in Series Circuit  Current in series circuit is same at all circuit elements VOLTAGE IN SERIES CIRCUIT  Voltage (V T ) in series circuit is the total of voltage for each elements.

5 Resistors in Parallel

6 Equivalent Resistors in Parallel:

7  Two resistors in parallel:

8 Current in Parallel Circuit  Currents in parallel circuit is the total of current for each elements. VOLTAGE IN PARALLEL CIRCUIT  Voltage (V T ) in parallel circuit is same at all circuit elements.

9 Example #1  Find the equivalent resistor (R eq ) in the circuit.

10 RESISTIVE CIRCUIT  Series/parallel resistor  Voltage divider circuit  Current divider circuit  Voltage and current measurement  Wheatstone bridge  Delta-wye (Pi-Tee) equivalent circuit

11 Voltage Divider 2 2 2

12  Using Ohm law, we will get:  Voltage at resistor R 2 :

13 RESISTIVE CIRCUIT Series/parallel resistorSeries/parallel resistor Voltage divider circuitVoltage divider circuit Current divider circuitCurrent divider circuit Voltage and current measurementVoltage and current measurement Wheatstone bridgeWheatstone bridge Delta-wye (Pi-Tee) equivalent circuitDelta-wye (Pi-Tee) equivalent circuit

14 Current Divider

15  From the Ohm’s law, (1)

16  Series/parallel resistor  Voltage divider circuit  Current divider circuit  Voltage and current measurement  Wheatstone bridge  Delta-wye (Pi-Tee) equivalent circuit RESISTIVE CIRCUIT

17 Voltage and Current Measurement  An ammeter is an instrument designed to measure current.  It is placed in series with the circuit element whose current is being measured.  An ideal ammeter has an equivalent resistance of 0Ω and functions as a short circuit in series with the element whose current is being measured.

18  A voltmeter is an instrument designed to measure voltage.  It is placed in parallel with the element whose voltage is being measured.  An ideal voltmeter has an infinite equivalent resistance and thus functions as an open circuit in parallel with the element whose voltage is being measured.

19  The configurations for an ammeter and voltmeter to measure current and voltage

20 RESISTIVE CIRCUIT  Series/parallel resistor  Voltage divider circuit  Current divider circuit  Voltage and current measurement  Wheatstone bridge  Delta-wye (Pi-Tee) equivalent circuit

21 Wheatstone Bridge  The Wheatstone bridge circuit is used to precisely measure resistance of medium values, that is in the range of 1Ω to 1MΩ.  The bridge circuit consists of four resistors, a dc voltage source and a detector.

22  The Wheatstone bridge circuit: Wheatstone Bridge

23  When the bridge is balanced:  Combining these equation, gives Wheatstone Bridge

24  Solving these equation, yields Wheatstone Bridge

25  Series/parallel resistor  Voltage divider circuit  Current divider circuit  Voltage and current measurement  Wheatstone bridge  Delta-wye (Pi-Tee) equivalent circuit RESISTIVE CIRCUIT

26 Delta-Wye (PI-TEE) Circuit  If the galvanometer in Wheatstone bridge is replace with its equivalent resistance R m,

27  The resistor R 1, R 2 and R m (or R 3, R m and R x ) are referred as a delta (∆) interconnection.  It is also referred as a pi (π) interconnection because the ∆ can be shaped into a π without disturbing the electrical equivalent of the two configurations.

28  Delta configuration

29  The resistors R 1, R m dan R 3 (or R 2, R m and R x ) are referred as a wye (Y) interconnection because it can be shaped to look like the letter Y.  The Y configuration also referred as a tee (T) interconnection.

30  Wye configuration

31 The ∆ - Y Transformation

32  Using series and parallel simplifications in Δ-connected, yield

33  Using straightforward algebraic manipulation gives,

34  The expression for the three Δ- connected resistors as functions of three Y-connected resistors are

35 Example #2  Find the current and power supplied by the 40 V sources in the circuit shown below.

36 Solution:  We can find this equivalent resistance easily after replacing either the upper Δ (100Ω, 125Ω, 25Ω) or the lower Δ (40Ω, 25Ω, 37.5Ω) with its equivalent Y.  We choose to replace the upper Δ. Thus, Example #2

37 Example #2

38  Substituting the Y-resistor into the circuit,

39  The equivalent circuit,

40  Calculate the equivalent resistance,  Simplify the circuit,

41  Then, the current and power values are,

42 Example #3 Find no load value of v o. Find vo when RL = 150 kΩ How much power is dissipated in the 25 kΩ resistor if the load terminals are short- circuited ?

43 a) b) Example #3

44 c) Example #3

45 Example #4  Find the power dissipated in the 6 Ω resistor.

46 Solution:  Equivalent resistance  current i o, Example #4

47  Note that i o is the current in the 1.6Ω resistor.  Use current divider to get current in the 6Ω resistor,  Then the power dissipated by the resistor is Example #4

48 Example #5  Find the voltage of v o and v g.

49 Solution:  Equivalent resistance  Current in resistor 30Ω Example #5

50  Voltage v 0  Total voltage at the resistor

51  Voltage v g

52 Example #6  Find the current of i g and io in the circuit. Solution:  Equivalent resistance:

53  The current values,  Thus, Example #6

54 Example #7  Determine the value of i o

55 Example #8  Find i and V o

56 Example #9  Calculate the value of current; I.