RESISTANCE CIRCUITS

RESISTANCE CIRCUITS Series/Parallel Resistor Circuit Voltage Dividers Circuit Current Dividers Measurement of Voltage and Current Wheatstone Bridge Equal Circuit Delta-Wye (Pi-Tee)

Series Resistor

Equivalent Resistance Req = R1 + R2 + ……….+ RN

Parallel Resistor

Equivalent Resistance

For two parallel resistor circuits

CIRCUITS VOLTAGE DIVIDER

By using Ohm’s law Voltage on resistor R2

Circuit Current Dividers

From Ohm’s law (1)

From equation (1)

Measurement of Voltage and Current 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.

Ammeter and Voltmeter configuration

WHEATSTONE BRIDGE

Galvanometer, G was connected between parallel path to detect equilibrium.

We found, I3 R3 = Ix Rx (1) Balance condition, voltage at R1 and R2 also should be same, I1 R1 = I2 R2 (2)

When no current go through Galvanometer, assume that, I1 = I3 (3) Change I3 with I1 and change IX with I2 .we have I1 R3 = I2Rx (4)

Devide eq. (2) and eq. (4), we have (5) We have, RX as

DELTA-WYE CIRCUITS(PI-TEE) Galvanometer in Wheatstone bridge circuit replace by resistor Rm ,

Resistor R1, R2 and Rm (or R3, Rm and Rx) called delta connection (∆) and also called pi (π) .

Configuration of delta circuit

Resistor R1, Rm and R3 (or R2, Rm and Rx) known as wye (Y) connection Resistor R1, Rm and R3 (or R2, Rm and Rx) known as wye (Y) connection. This configuration also known as tee (T) connection.

Configuration of wye circuit

∆ - Y equivalent circuit

By using series-parallel theory, equivalent resistance in ∆ circuit for every terminal pair

From previous three equation, we have

For Y - ∆ circuits. Y circuits change to ∆ circuit and every path could be found like below.

EXAMPLE 1

From previous circuit, calculate. v0 if RL not connected v0 if RL = 150kΩ Power absorbed by 25kΩ resistor if terminal load was close circuit.

Answer a) b)

c)

EXAMPLE 2 Calculate power that absorb by resistor 6Ω resistor

Answer Equivalent resistor find i0,

If current that flows through 1 If current that flows through 1.6Ω resistor is i0, current that flows through 4Ω and 6Ω resistor can be calculated

Power that obsorb by 6Ω resistor could be calculated as below,

Example 3 Calculate current and power that have been supplied by power supply 40V.

We can select to have above delta connection (100, 125, 25Ω) or below delta connection (40, 25, 37.5Ω) and change to Y connection. Here we select above delta connection.

Insert Y resistance in the circuit

Equivalent resistance,

Circuit

Equivalent circuit

Current I and power absorb by circuit

Example 3

Answer Equivalent resistance Current at 30Ω resistor

v0 Total drop voltage at resistor

vg

Example 4

Answer Equivalent resistance

Then

thus

QUIZ 2

QUIZ 3