Parallel Circuits ELPT 1311 Basic Electrical Theory Chapter

Parallel Circuits ELPT 1311 Basic Electrical Theory Chapter 06_Parallel Curcuits Introduction to Electricity by Paynter & Boydell and Pearson Illustrations

Objectives • • Identify a parallel circuit • Calculate any current value in a parallel circuit given the source voltage and the branch resistances • • • Describe current and voltage characteristics of parallel circuits Contrast the current and voltages of series & parallel Calculate the total resistance in any parallel circuit, given the branch resistances Calculate the current, voltage, power, and resistance of any parallel circuit Describe the procedure to locate an open parallel circuit branch Describe the symptoms for a parallel short circuit branch

Parallel Circuits Voltage and Current • Current in series circuits only have one path to flow, but in parallel circuits there are two or more paths for current to flow. • In the three resistor parallel circuit: • • Current leaving the voltage source travels to the first junction (Point A) and then splits with part of the current flowing through Branch 1 and the remainder of the current flowing to Point C Current splits again at point C with part of the current flowing through Branch 2 and the remainder of the current flowing toward Point E Current then flows through Branch 3 All the branch currents then combine at Points B, D, and F, and flow back to the voltage source

Parallel Circuits Voltage and Current • A parallel circuit can be viewed as a current divider because the source current is divided among the branches in the circuit IT = IR 1 + IR 2 + IR 3 + … + IRn

Parallel Circuits Voltage and Current • What is the value of the circuit current? IT = IR 1 + IR 2 + IR 3 + … + IRn IT = 5 A + 11 A + 900 m. A IT = 5 A + 11 A + 0. 9 A IT = 16. 9 A

Parallel Circuits Voltage and Current • What is the value of the circuit current?

Parallel Circuits Voltage and Current • What is the value of the circuit current? IT = 6. 4 A + 3. 2 A +. 8 A IT = 10. 4 A

Parallel Circuits Voltage and Current • In series circuits each resistor has a voltage drop proportional to its value in ohms, but in parallel circuits each branch of the circuit has the same voltage drop • When two or more components are connected in parallel, the voltage across each component is equal to the voltage across the others • In the three resistor parallel circuit: • Because the resistance in each branch is known and voltage is known, current through each branch can be calculated using ohms law • Voltage is the same across R 1, R 2, and R 3 because each branch is connected across the voltage source

Parallel Circuits Voltage and Current E = VT = VR 1 = VR 2 = VR 3 = … = VRn and: IRn = E / Rn

Parallel Circuits Voltage and Current • What is the value of current through each branch and what is the total current?

Parallel Circuits Voltage and Current • • To the same circuit another branch is added with 200 Calculate the current through R 3 Did adding another branch (increase) or (decrease) IT? Did adding another branch (increase) or (decrease) RT?

Parallel Circuits Voltage and Current • What is the value of current through each branch and what is the total current? 48 200 300

Parallel Circuits Voltage and Current • What is the value of current through each branch and what is the total current? 240 300

Parallel Circuits Voltage and Current • What is the value of current through each branch and what is the total current?

Parallel Circuits Voltage and Current

Parallel Circuits Resistance • In series circuits the total resistance is the sum of all the resistances o But in parallel circuits the total resistance in the circuit is always less than the resistance of the branch with the smallest resistance • Consider a series circuit with R 1 at 10 connected across a 10 V voltage source; the resultant current is 1 A 1 A

Parallel Circuits Resistance • Now connect another 10 resistor ( R 2 ) parallel to R 1 ; the resultant current is 2 A • It stands to reason that when R 2 was added, another path for current flow was created causing current to increase • By doing a circuit analysis it can be seen that total resistance is less that either R 1 or R 2 • Taking this to its logical conclusion: o Adding parallel branches to a circuit results in a reduction of circuit resistance regardless of how large or small the resistance is of the added branch

Parallel Circuits Resistance – Ohms Law 2 A

Parallel Circuits Resistance – Ohms Law • Find circuit resistance by calculating branch currents, and then using ohms law calculate circuit resistance

Parallel Circuits Resistance – Reciprocal Approach • Total resistance can be calculated without having the current value through each branch by using any of the three methods outlined in this instruction • 1 st method is the "Reciprocal Approach" that can be used for any number of resistors o The reciprocal approach formula: rewritten

Parallel Circuits Resistance – Reciprocal Approach • • On a previous slide the circuit below was found to have 12 using current and voltage in the calculation Here we use the reciprocal approach • Calculator key strokes

Parallel Circuits Resistance – Reciprocal Approach • Calculate RT using the reciprocal approach 24 k 26 k 980

Parallel Circuits Resistance – Reciprocal Approach • Calculate RT using the reciprocal approach 5 30 26 k 980 60

Parallel Circuits Resistance – Reciprocal Approach • Calculate RT using the reciprocal approach 182 V 2. 5 k 1. 3 k 650 925

Parallel Circuits Resistance • For the same circuit, calculate total resistance using ohms law to verify the resistance calculated by the reciprocal approach 182 V 2. 5 k 1. 3 k 650 925

Parallel Circuits Resistance – Product / Sum Approach • 2 nd method is the "Product Over Sum Approach" o The product over sum is used to find the RT of two branches :

Parallel Circuits Resistance – Product / Sum Approach • Find RT for the circuit below using the product / sum approach 500 k 50 k

Parallel Circuits Resistance – Product / Sum Approach • Find RT for the circuit below using the product / sum approach 45 90

Parallel Circuits Resistance – Product / Sum Approach • Find RT for the circuit below using the product / sum approach

Parallel Circuits Resistance • For the same circuit, calculate total resistance using ohms law to verify the resistance calculated by the product over sum approach

Parallel Circuits Resistance - • 3 rd method is the "Equal Branch Resistance Approach" o The equal branch resistance is used when all the branches of a parallel circuit have the same resistance :

Parallel Circuits Resistance - • Use the equal branch resistance approach to find RT 27. 5 27. 5

Parallel Circuits Resistance

Parallel Circuits - Power • The same power formulas are used in parallel circuits but the way power behaves is different as compared to a series circuit

Parallel Circuits - Power • In series circuits: o The "lower" the value of resistance, the "less" power it dissipates because current is the same through all resistors • In parallel circuits, the opposite is true: o The "lower" the value of the branch resistance, the "more" power it dissipates because current through the branch resistor increases • To illustrate consider the series and parallel circuits both having the same power source and same resistance values o Series circuit: § The 100 ohm resistor is dissipating 100 watts and the 50 ohm resistor is dissipating 50 watts. o Parallel circuit: § The 100 ohm resistor is also dissipating 100 watts but the 50 ohm resistor is dissipating 450 watts.

Parallel Circuits - Power

Parallel Circuits - Power • Find total power and verify with voltage and current or

Parallel Circuits - Power • What would the R 2 wattage be in the same circuit if R 2 resistance was reduced to 25 , by how much did it decrease or increase, and what is the value PS? R 2 DECREASES FROM 50 TO 25

Parallel Circuits - Power • What would the R 2 wattage be in the same circuit if R 2 resistance was reduced to 25 , by how much did it decrease or increase, and what is the value PS? One half the resistance increased power 2 times R 2 DECREASES FROM 50 TO 25

Parallel Circuits - Power • Calculate total resistance, branch currents, total current, branch powers, and total power (check with RT IT PT & E) RT = ______ IR 1 = ______ IR 2 = ______ IR 3 = ______ IT = ______ PR 1 = ______ PR 2 = ______ PR 3 = ______ PT = ______

Parallel Circuits - Power • Calculate total resistance, branch currents, total current, branch powers, and total power (check with RT IT PT & E)

Parallel Circuits - Power • Calculate total resistance, branch currents, total current, branch powers, and total power (check with RT IT PT & E) RT = ______ IR 1 = ______ IR 2 = ______ IR 3 = ______ IT = ______ PR 1 = ______ PR 2 = ______ PR 3 = ______ PT = ______

Parallel Circuits - Power • Calculate total resistance, branch currents, total current, branch powers, and total power (check with RT IT PT & E)

Parallel Circuits – Current Dividers • Kirchhoff’s current law (KCL) describes the relationship between the various currents in a parallel circuit • KCL states … the current leaving any point in a circuit is equal to the current entering the point • The points where two or more current paths are connected are called nodes.

Parallel Circuits – Current Dividers • • Using KCL an unknown resistance can be determined. Consider the circuit below with the rheostat adjusted to provide an IT of 2. 8 amp, what resistance is the rheostat adjusted to?

Parallel Circuits – Current Dividers • Consider the circuit below with the rheostat adjusted to provide an IT of 124 m. A, what resistance is the rheostat adjusted to?

Parallel Circuits – Current Dividers • Consider the circuit below with the rheostat adjusted to provide an IT of 160 m. A, what resistance is the rheostat adjusted to?

Parallel Circuits – Current Sources • • • A constant current source (regulated current source power supply) is a source that is designed to provided an output current value that remains fairly constant over a wide range of load resistance values As RL increases or decreases the regulated current source will maintain 10 m. A resulting in a corresponding increase or decrease in the voltage drop across RL Consider IS regulating at 10 m. A in the series circuit

Parallel Circuits – Current Sources • A regulated current source used in a parallel circuit presents a little more complicated approach to determining the voltage drops • Since the current stays constant under changing loads the source voltage (voltage across the branches) must change to maintain the specified current flow

Parallel Circuits – Current Sources • Find the source voltage for the regulated current circuit below

Parallel Circuits – Fault Symptoms - Opens • • In series circuits, an open circuit totally stops current flow and all resistance voltage drops go to zero An open in a parallel circuit is more difficult to find because the branch voltage will still be source voltage OPEN SERIES CIRCUIT OPEN PARALLEL CIRCUIT

Parallel Circuits – Fault Symptoms - Opens • Too find an open branch in a parallel circuit disconnect one branch at a time; current will increase each time a good branch is lifted and not change when the open branch is lifted. A – normal current A B – less current B

Parallel Circuits – Fault Symptoms - Shorts • • Shorts will cause a circuit overcurrent protective device such as a fuse to open Voltage drop across all branches go to zero

Complete Chapter 6 Review Read Chapter 7 Introduction to Series Parallel Circuits