EKT101 Electric Circuit Theory Chapter 2 Resistive Circuits

Overview of Chapter 2 2.1 Series Resistors and Parallel Resistors 2.2 Voltage Divider Circuit 2.3 Current Divider Circuit 2.4 Voltage and Current Measurement 2.5 Wheatstone Bridge 2.6 Wye-Delta Transformations.

Resistors

2.1 Series and Parallel Resistors (1) Series Resistors Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current. The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances.

Series Resistors in Circuit The potential difference between the terminals of the battery (V) equals the sum of the potential differences across the resistors.

2.1 Series and Parallel Resistors (2) Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them. The equivalent resistance of a circuit with N resistors in parallel is:

Parallel Resistors in Circuit The supply current (I) equals the sum of the currents in the branches.

2.1 Series and Parallel Resistors (3) Example Find Req in circuit below.

2.1 Series and Parallel Resistors (4) Example Find Req in circuit below.

2.2 Voltage Divider Circuit (1) The voltage divider for N series resistors can be expressed as

2.2 Voltage Divider Circuit (2) To determine the voltage across each resistor.

2.2 Voltage Divider Circuit (3) Apply KVL to the circuit; From Ohm’s law, From KVL, therefore, Solving equation for current, Apply Ohm’s law to determine voltage across each resistor;

2.3 Current Divider Circuit (1) The total current, I is shared by the resistors in inverse proportion to their resistances. The current divider can be expressed as:

2.3 Current Divider Circuit (2) To determine the current flow on each resistor.

2.3 Current Divider Circuit (3) Apply KCL, Using ohm’s law on each branch, therefore Current flow through each branch,

Example (voltage divider) Determine vo and io in the circuit below.

2.4 Voltage and Current Measurement An ammeter is an instrument designed to measure current and is placed in series with the circuit element. A voltmeter is an instrument designed to measure voltage and is placed in parallel with the element.

2.5 Wheatstone Bridge A Wheatstone bridge circuit is an accurate device for measuring resistance

Under balance condition where no current flow between BD, Current in each resistance arm, Therefore,

2.6 Wye-Delta Transformations

Y-Δ Transformations

Example Transform Y circuit to Δ circuit

Δ - Y Transformations

Example Calculate the current and power supplied by the 40 V sources.

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

Example #2 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

Substituting the Y-resistor into the circuit,

The equivalent circuit,

Calculate the equivalent resistance, Simplify the circuit,

Then, the current and power values are,

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

Example #3 a) b)

Example #3 c)

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

Example #4 Solution: Equivalent resistance current io,

Example #4 Note that io 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 #5 Find the voltage of vo and vg.

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

Voltage v0 Total voltage at the resistor

Voltage vg

Example #6 Find the current of ig and io in the circuit. Solution: Equivalent resistance:

Example #6 The current values, Thus,

Example #7 Determine the value of io

Example #8 Find i and Vo

Example #9 Calculate the value of current; I.