RESISTIVE CIRCUIT Topic 2

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

SERIES/PARALLEL RESISTOR Resistors in series: Resistance equivalent Req = R1 + R2 + ……….+ RN

CURRENT IN SERIES CIRCUIT Current in series circuit is same at all circuit elements VOLTAGE IN SERIES CIRCUIT Voltage (VT) in series circuit is the total of voltage for each elements.

Resistors in parallel:

Resistance equivalent:

Two resistors in parallel:

CURRENT IN PARALLEL CIRCUIT Currents in parallel circuit is the total of current for each elements. VOLTAGE IN PARALLEL CIRCUIT Voltage (VT) in parallel circuit is same at all circuit elements.

Example Find Req.

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

VOLTAGE DIVIDER 2 2 2

Using Ohm law, we will get: Voltage at resistor R2:

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

CURRENT DIVIDER

Using Ohm law, (1)

From equation (1):

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

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.

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.

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

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

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.

The Wheatstone bridge circuit:

When the bridge is balanced: Combining these equation, gives

Solving these equation, yields

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

DELTA-WYE (PI-TEE) CIRCUIT If the galvanometer in Wheatstone bridge is replace with its equivalent resistance Rm,

The resistor R1, R2 and Rm (or R3, Rm and Rx) are referred as a delta (∆) interconnection. It also is referred as a pi (π) interconnection because the ∆ can be shaped into a π without disturbing the electrical equivalance of the two confiurations.

Delta configuration

The resistors R1, Rm dan R3 (or R2, Rm and Rx) 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.

Wye configuration

The ∆ - Y transformation

Using series and parallel simplifications in Δ-connected, yield

Using straightforward algebraic manipulation gives,

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

EXAMPLE 1 Find the current and power supplied by the 40V sources in the circuit shown below.

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

Substituting the Y-resistor into the circuit,

The equivalent circuit,

Calculate the equivalent resistance,

Simplification of the circuit,

Then, the current and power values are,

Example 2

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

Answer: a) b)

c)

EXAMPLE 3 Find the power dissipated in the 6Ω resistor.

Equivalent resistance Answer Equivalent resistance current io,

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 4 Find the voltage of vo and vg.

Answer Equivalent resistance Current in resistor 30Ω

Voltage v0 Total voltage at the resistor

Voltage vg

EXAMPLE 5 Find the current of ig and.io

Equivalent resistance: Answer Equivalent resistance:

Current values,

Thus,

EXAMPLE 6 Determine the value of io

Example 7 Find i and Vo

Example 8 Calculate the value of I.