AS

310102d Series Resistive Circuits 2017 (TF)

Series Resistive Circuits

Instrumentation Technician

  • Focus on understanding series resistive circuits.

Objectives

  • Define a series circuit and calculate the current within it.

  • State the formula for total resistance and calculate resistance in a series circuit.

  • State and apply Kirchhoff’s Voltage Law to series circuits.

  • Define terms such as ratio and direct proportion, perform calculations using both.

  • State the relationship between resistive values of components and their voltage drops; solve using the divider rule.

  • Determine voltage drops across a closed or open circuit component in a series circuit.

Key Concepts

Series Circuits

  • Definition: A series circuit is a complete electrical path allowing current to flow with only one route available.

  • Components Required:

    • Voltage source (potential difference)

    • Conductive path

    • Amount of resistance (load)

  • Illustration: Basic components include battery (voltage source), conductors (path), and resistors (load).

Properties of Current in a Series Circuit

  • Current labeling: Current through components is labeled (e.g., I1 for R1, I2 for R2, etc.).

  • Supply current:** Total current (IT) is equal for all components:**

    • IT = I1 = I2 = I3

Properties of Resistance in a Series Circuit

  • Each resistor added increases total resistance offering more obstruction to current.

  • Total Resistance Formula: RT = R1 + R2 + R3 + ...

Kirchhoff’s Voltage Law

  • Definition: The applied voltage equals the sum of the voltage drops in a closed loop.

    • E = V1 + V2 + V3

    • Algebraically, E - (V1 + V2 + V3) = 0.

Kirchhoff’s Current Law

  • Defines the behavior at a junction: Total current entering must equal total current leaving.

  • For series circuits, IT = I1 = I2 = I3.

Ratio & Direct Proportion

  • Ratio: Comparison between quantities, shown as:

    • 3:1

    • 3 to 1

    • 3/1

  • Direct Proportion: One quantity increases with another at the same rate, denoted as ∝.

    • Example: Earnings are directly proportional to hours worked.

Voltage Divider Rule

  • In a series circuit, the divider rule helps find voltage drops using Ohm's Law.

  • Formulas include:

    • IT = I1 = I2

    • V1/R1 = V2/R2 (voltage division).

Example Calculation Using Voltage Divider Rule

  • Given values: V1 = 20V, R1 = 10Ω, R2 = 30Ω.

  • Calculate voltage across R2 using relationships from the divider rule.

Voltage Drops in a Closed Circuit

  • A closed circuit allows current flow; applies Kirchhoff’s Voltage Law:

    • E = (V1 + V2 + V3).

    • A closed switch acts as a conductor with negligible resistance.

Voltage Drops in an Open Circuit

  • Switch open: Acts like an open conductor; no current flow and no voltage drops:

    • Example: V2 = I2 x R2 = 0V if no current flows.

Series Circuit Formulas

  • Formulas reviewed:

    • IT = I1 = I2 = I3 = ...

    • ET = V1 + V2 + V3 + ...

    • RT = R1 + R2 + R3 + ...

Steps for Series Circuit Calculation

  1. Redraw Circuit: Use a single line diagram to show connections.

  2. Total Resistance Calculation: Add resistances: RT = R1 + R2 + R3 (e.g., = 60Ω).

  3. Calculate Total Current: Use Ohm's law:

    • I = E/R (e.g. I = 10V / 60Ω = 0.166A).

  4. Calculate Voltage Drops Across Each Resistor:

    • V = I x R (e.g. V1 = 20Ω x 0.166A = 3.32V).

Final Values from Calculation

  • For the circuit of three 20Ω resistors with a 10V supply:

    • ET = 10V, IT = 0.166A, RT = 60Ω

    • V drops across R1, R2, R3 = 3.32V each.