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.