310102e Parallel Resistive Circuits 2017 (TF)

Instrumentation Technician: Parallel Circuits

Page 1: Introduction

• Course Code: 310102e

• Topic: Parallel Circuits

Page 2: Objectives

• Key Learning Goals:

  • Define a parallel circuit.

  • Calculate total resistance using formulas.

  • Describe and apply Kirchhoff's Current Law (KCL) in parallel circuits.

  • Analyze the effects of open circuits.

  • Use the current divider principle for branch circuit calculations.

Page 3: Understanding Parallel Circuits

• Definition: A parallel circuit allows current to flow through multiple branches connected to the same voltage source.

• Components of a Parallel Circuit:

  • Voltage Source (potential difference)

  • Conductive Paths (wires)

  • Resistance (load)

Page 4: Components Illustrated

• Example of a parallel circuit:

  • Voltage Source: Battery

  • Conductive Paths: Three wires/branches

  • Load: Resistors

Page 5: Voltage Properties in Parallel Circuits

• Equal Voltage: Each branch voltage equals the supply voltage

  • Example: Each branch (1, 2, 3) has a voltage drop of 120V.

  • General Rule: E = V1 = V2 = V3

Page 6: Resistance Properties in Parallel Circuits

• Effect of Adding Resistors: Each added resistor creates an additional path for current, increasing overall current.

• Ohm's Law Relation:

  • Increased current implies decreased total resistance if voltage remains constant.

Page 7: Reciprocal Sum Formula

• Formula for Total Resistance (RT):

  • RT = 1 / (1/R1 + 1/R2)

  • Example: RT = 1 / (1/15 + 1/30) = 10Ω

Page 8: Kirchhoff's Voltage Law (KVL)

• KVL Statement: The sum of voltages in a closed loop is zero.

  • E - (V1 + V2 + V3) = 0

  • Applied voltage equals each parallel branch voltage drop: E = V1 = V2 = V3

Page 9: Kirchhoff's Current Law (KCL)

• KCL Statement: The current entering a junction is equal to the current leaving.

  • Example: 24A enters at Point A, splits into 18A at Point B and 6A at Point D.

  • Verification: 18A + 6A = 24A

Page 10: Line and Branch Currents

• Current Flow: Total current (IT) equals the sum of branch currents:

  • IT = I1 + I2 + I3...

  • Important principle: What goes in must come out.

Page 11: Open Circuit Effects

• Impact of Open Circuits:

  • Total current decreases by the amount flowing through the open branch.

  • Total resistance increases, following Ohm's Law: increased resistance = decreased current.

Page 12: Example of Open Circuit Effects

• In a circuit with IT = 24A:

  • Current distribution before opening:

    • I1 = 6A, I3 = 10A, I2 = 8A

  • If branch 2 disconnects, IT decreases by 8A.

Page 13: Current Divider Principle

• Basic Principle: Current is inversely proportional to resistance.

  • If resistance increases, current decreases.

• Mathematical statement: I2 = R1/(R2 + R1) * I1

Page 14: Current Divider Principle Example

• Calculation: Using prior knowledge:

  • Set up: I2 = R1/(R1 + R2) * I1

  • Example calculation results in R2 being 7.5Ω.

Page 15: Summary of Parallel Circuit Formulas

• Key Formulas:

  • IT = I1 + I2 + I3 + I4...

  • ET = V1 = V2 = V3...

  • Total Resistance: RT = 1 / (1/R1 + 1/R2 + 1/R3...)

Page 16: Combining Definitions and Laws

• Unified Statements:

  • Currents entering and leaving each junction must equal: IT = I1 + I2 + I3...

  • Each branch voltage drop equals applied voltage: ET = V1 = V2 = V3...

  • RT calculation reflects the reciprocals of individual resistances.

Page 17: Solving Parallel Circuits

• Approach:

  • Use Ohm's Law to find values branch by branch, then summarize totals.

  • Look for two of the three values (current, voltage, resistance) to find the third.

Page 18: Parallel Circuit Calculation Example

• Sample Circuit: Three resistors (R1, R2, R3) each 20Ω in parallel with a 10V supply.

Page 19: Drawing the Circuit

• Visual Representation:

  • Resistors visualized with corresponding values and arrangement.

Page 20: Determining Current for Each Resistor

• Using Ohm's Law:

  • I1 = 10V / 20Ω = 0.5A for each resistor.

  • Total Current IT = 0.5A + 0.5A + 0.5A = 1.5A.

Page 21: Calculating Total Resistance

• Using Reciprocal Formula:

  • Total resistance calculated at 6.66Ω, always less than the smallest resistor in parallel.

Page 22: Validating Total Current

• Checking with Ohm's Law:

  • Confirm IT = 1.5A using RT = 6.66Ω and voltage:

    • I = E/R = 10V / 6.66Ω = 1.501A.

Page 23: Final Output Values

• Calculated Values:

  • ET = 10V DC

  • IT = 1.5A

  • RT = 6.66Ω

  • Each resistor voltage: V1 = V2 = V3 = 10V, Current: I1 = I2 = I3 = 0.5A with each R = 20Ω.