310102f Series - Parallel Resistive Circuits 2017 (TF)
Page 1: Introduction to Series-parallel Resistive Circuits
Course Title: Instrumentation Technician 310102f
Focus: Understanding series-parallel resistive circuits.
Page 2: Objectives
Students will gain the ability to:
Identify resistors in series.
Identify resistors in parallel.
Calculate total resistance in a series-parallel circuit.
Apply Kirchhoff’s Current Law.
Apply Kirchhoff’s Voltage Law.
Solve problems related to series-parallel circuits.
Page 3: Understanding Series-parallel Circuits
A circuit is a complete path for current flow.
Series-parallel circuit: Multiple paths for current flow and different branch voltages.
Essential components of an electrical circuit:
A voltage source (potential difference).
A conductive path.
An amount of resistance (a load).
Page 4: Components of a Series-parallel Circuit
This type of circuit includes:
A voltage source (battery).
A conductive path (conductors).
Resistance elements (resistors).
Page 5: Identifying Series Resistances
Current flows through R1 at junction A, branching to R2 and R3.
Current reunites at junction B, making R1 in series with parallel resistors R2 and R3.
Page 6: Calculating Series Resistances
Identify series resistances using the Series Circuit Resistance Formula:
IT = I1 = I2 = I3 = I4... (same current through series resistors)
ET = V1 + V2 + V3 + V4... (total voltage is the sum of individual voltages)
RT = R1 + R2 + R3 + R4... (total resistance is the sum of series resistances).
Page 7: Identifying Parallel Resistances
At junction A, current splits into two paths through R2 and R3.
The endpoint of current division indicates parallel resistance:
R2 and R3 are in parallel.
Page 8: Calculating Parallel Resistances
Use the Parallel Circuit Resistance Formula to calculate equivalent values:
IT = I1 + I2 + I3 + I4... (total current is the sum of individual currents).
ET = V1 = V2 = V3 = V4... (voltage is the same across parallel resistors).
Ensure any series resistances are calculated first before combining with parallel resistances.
Page 9: Steps to Calculate Total Resistance
Steps to find the equivalent total resistance:
Perform a series resistance calculation for connected series resistors.
Use this resulting equivalent resistance for parallel resistance calculations.
Alternate between parallel and series calculations to derive total resistance (RT).
Page 10: Example Circuit Calculation
Given: A series/parallel circuit with three resistors across a 10 volt DC supply.
Page 11: Drawing the Circuit
Redraw the circuit in a single line diagram to view connections clearly.
Three resistors depicted in series-parallel configuration.
Page 12: Adding Parallel Resistors
Calculate parallel resistors R2 and R3 first,
Utilize the parallel resistance formula:
1/R_total = 1/R2 + 1/R3.
Page 13: Series Addition
Recognizing that R1 is in series with the equivalent resistance of R2 and R3, perform series calculations:
RT = R1 + R2,3.
Page 14: Total Resistance and Current Calculation
Performing addition:
RT = R1 + R2,3 -> If RT = 30 ohms, then:
IT = E / RT = 10V / 30 ohms = 0.3333 A (or 333.3 mA).
Page 15: Working Back Through the Circuit
Calculate voltage drops:
V1 = I1 x R1 = 0.333 x 20 ohms = 6.66V.
V2,3 = I2,3 x R2,3 = 0.333 x 10 ohms = 3.33V.
Note: 3.33 volts is across the combination of R2 and R3 in parallel.
Page 16: Final Circuit Connections
Diagram indicates battery terminals expanded across the diagram:
Confirm resistances and currents calculated:
IT = 0.3333A, ET = 10VDC, RT = 30 ohms.
Page 17: Summary of Circuit Values
Completed calculations:
IT = 0.3333A, ET = 10 VDC, RT = 30 ohms.
Resistor values:
R1 = 20 ohms, V1 = 6.66 VDC.
R2 = 20 ohms, I2 = 0.1665 A, V2 = 3.33 VDC.
R3 = 20 ohms, I3 = 0.1665 A, V3 = 3.33 VDC.