Lecture No. 3 - Introduction to Electrical Engineering

SIMATIC HMI Overview

• Title: SIMATIC HMI

• Presented by: Dr. Essam Nabil

• Institution: Menoufia University, Faculty of Applied Health Sciences Technology

• Date: 23 October 2023

Presentation Scope

1. Resistors

2. Kirchhoff's Voltage Law

3. Voltage Sources in Series

4. Voltage Dividers

5. Power in Series

6. Parallel Resistors

7. Kirchhoff's Current Law

8. Voltage Sources in Parallel

9. Current Dividers

10. Power in Parallel

11. Conductance

12. Loading Effects

13. Series-Parallel Circuits

14. Thanks & Questions

Resistors

Series Resistors

• Definition: Series circuit configuration with elements connected end-to-end.

• Equivalent Resistance:

  • Formula: ( R_{equiv} = R_1 + R_2 + R_3 + ... + R_N )

  • Relation: ( V = I R_{equiv} )

Current Flow in Series Resistors

• Current is the same through each resistor:

  • Relation: ( I = I_1 = I_2 = ... = I_N )

• Voltage across each resistor follows:

  • ( \frac{V_n}{R_n} = I ) for all n.

Voltage Drops in Series Resistors

• Relation: ( E = V_1 + V_2 + V_3 + ... + V_N )

  • Where ( E ) is the total emf applied.

Kirchhoff’s Laws

Kirchhoff's Voltage Law (KVL)

• Statement: The algebraic sum of all voltages around a closed path equals zero.

  • Formula: ( \sum_{n=1}^{N} V_n = 0 )

  • Application: ( -E + V_1 + V_2 + V_3 = 0 )

Kirchhoff's Current Law (KCL)

• Statement: The algebraic sum of currents entering a node equals the sum of currents leaving that node.

  • Formula: ( \sum_{n=1}^{N} I_n = 0 )

Voltage Sources in Series

• When multiple voltage sources are connected in series, they can be replaced by a single source whose value is the sum or difference of the individual sources.

Voltage Dividers

• Purpose: Obtain a specific voltage from a larger supply voltage using resistors in series.

• Formula for output voltage:

  • ( V_1 = \frac{E R_1}{R_1 + R_2} )

Power in Series

• Total power in a series circuit equals the sum of power dissipated in each resistor:

  • Formula: ( P_T = P_1 + P_2 + ... + P_N )

• Relation between power, voltage, and resistance:

  • ( P = \frac{V^2}{R} ) and ( P = I^2 R )

Parallel Resistors

Configuration and Equivalence

• Definition: Parallel circuit with elements connected side-by-side.

  • Formula for equivalent resistance:( \frac{1}{R_{equiv}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_N} )

Voltage and Current in Parallel Resistors

• The same voltage is developed across each resistor:

  • ( V = V_1 = V_2 = ... = V_N )

• Total current is the sum of the individual branch currents:

  • ( I = I_1 + I_2 + ... + I_N )

Current Dividers

• Necessary to divide current among different paths in a circuit:

  • Basic principle: The current delivered to an element is proportional to its conductance.

Power in Parallel

• Total power is the sum of power dissipated by each resistor:

  • Formula: ( P_T = P_1 + P_2 + ... + P_N )

Conductance

• Conductance is the reciprocal of resistance:

  • Formula: ( G = \frac{1}{R} )

  • Relationship: ( G_{equiv} = G_1 + G_2 + ... + G_N )

Examples

Example 2.1

• Calculate current through four series-connected resistors with known values and verify sum equals supply voltage.

Example 2.9

• Determine voltage levels and power dissipation across individual resistors for given circuit parameters.

Example 2.22

• Calculate the power dissipated in parallel resistors and discussion on conductance values.

Conclusion

• Summary of significant laws and applications in circuits.

• Acknowledgment of the audience and encouragement for further learning.