EEC 115 - Electrical Engineering Fundamentals

EEC 115 - Tushen Injiniyan Lantarki

Comprehensive Study Guide for ND1 Students

Jagorar Nazari Cikakke ga Daliban ND1

Ohm's Law and Basic Circuits

Dokar Ohm da Da'irori na Asali

Ohm's Law: States that current (I) is directly proportional to voltage (V) and inversely proportional to resistance (R).

Dokar Ohm: Ta bayyana cewa halin yanzu (I) yana daidai da ƙarfin lantarki (V) kuma yana saba wa juriya (R).

I = V / R

V = I × R

R = V / I

Example: Calculating Resistance

Misali: Lissafin Juriya

If V = 100V and I = 5mA, find R.

Idan V = 100V da I = 5mA, nemo R.

Step 1: Convert mA to A: I = 5 × 10⁻³ A = 0.005 A

Mataki na 1: Canza mA zuwa A: I = 5 × 10⁻³ A = 0.005 A

Step 2: Apply Ohm's Law: R = V / I = 100 / 0.005 = 20,000 Ω = 20 kΩ

Mataki na 2: Aiwatar da Dokar Ohm: R = V / I = 100 / 0.005 = 20,000 Ω = 20 kΩ

Important: Always ensure units are consistent (Volts, Amperes, Ohms) before applying Ohm's Law.

Muhimmi: Koyaushe tabbatar raka'a sun yi daidai (Volts, Amperes, Ohms) kafin a yi amfani da Dokar Ohm.

Series and Parallel Circuits

Da'irori na Jere da Na Kusa

Series Circuits

Da'irori na Jere

Only one path for current flow
Current is the same through all components
Total resistance: R_total = R₁ + R₂ + R₃ + ...
Voltage divides across components

Hanya ɗaya kawai don kwararar halin yanzu
Halin yanzu yayi daidai a cikin duk abubuwan
Jimlar juriya: R_total = R₁ + R₂ + R₃ + ...
Ƙarfin lantarki yana raba a kan abubuwan

Parallel Circuits

Da'irori na Kusa

Multiple paths for current flow
Voltage is the same across all components
Total resistance: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
Current divides between branches

Hanyoyi da yawa don kwararar halin yanzu
Ƙarfin lantarki yayi daidai a kan duk abubuwan
Jimlar juriya: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
Halin yanzu yana raba tsakanin rassan

Example: Series Circuit Calculation

Misali: Lissafin Da'irar Jere

Given R₁ = 2.2Ω, R₂ = 1.8Ω, and V = 12V, find voltage drops across each resistor.

An bayar da R₁ = 2.2Ω, R₂ = 1.8Ω, da V = 12V, nemo raguwar ƙarfin lantarki a kowane resistor.

Step 1: Calculate total resistance: R_T = R₁ + R₂ = 2.2 + 1.8 = 4Ω

Mataki na 1: Lissafa jimlar juriya: R_T = R₁ + R₂ = 2.2 + 1.8 = 4Ω

Step 2: Calculate current: I = V / R_T = 12 / 4 = 3A

Mataki na 2: Lissafa halin yanzu: I = V / R_T = 12 / 4 = 3A

Step 3: Calculate voltage drops: V_R1 = I × R₁ = 3 × 2.2 = 6.6V, V_R2 = I × R₂ = 3 × 1.8 = 5.4V

Mataki na 3: Lissafa raguwar ƙarfin lantarki: V_R1 = I × R₁ = 3 × 2.2 = 6.6V, V_R2 = I × R₂ = 3 × 1.8 = 5.4V

Resistivity and Conductivity

Juriya da Gudanarwa

Resistivity (ρ): The resistance of a material of unit length and unit cross-sectional area.

Juriya (ρ): Juriya na wani abu mai tsayi na raka'a da yanki na giciye na raka'a.

ρ = R × A / l

where: R = resistance, A = cross-sectional area, l = length

Conductivity (σ): The reciprocal of resistivity, measures how well a material conducts electricity.

Gudanarwa (σ): Ma'anar juriya, yana auna yadda wani abu yake gudanar da wutar lantarki.

σ = 1 / ρ

Example: Calculating Resistivity

Misali: Lissafin Juriya

A wire of length 0.5m, diameter 0.5mm, has resistance of 2.5Ω. Calculate resistivity.

Waya mai tsayi 0.5m, diamita 0.5mm, yana da juriya 2.5Ω. Lissafa juriya.

Step 1: Calculate radius: r = 0.5mm / 2 = 0.25mm = 2.5 × 10⁻⁴ m

Mataki na 1: Lissafa radius: r = 0.5mm / 2 = 0.25mm = 2.5 × 10⁻⁴ m

Step 2: Calculate cross-sectional area: A = πr² = (22/7) × (2.5 × 10⁻⁴)² m²

Mataki na 2: Lissafa yankin giciye: A = πr² = (22/7) × (2.5 × 10⁻⁴)² m²

Step 3: Calculate resistivity: ρ = R × A / l = 2.5 × (22/7) × (2.5 × 10⁻⁴)² / 0.5 = 98.19 × 10⁻⁸ Ω·m

Mataki na 3: Lissafa juriya: ρ = R × A / l = 2.5 × (22/7) × (2.5 × 10⁻⁴)² / 0.5 = 98.19 × 10⁻⁸ Ω·m

Temperature Coefficient of Resistance

Ma'aunin Zafin Jiki na Juriya

Definition: The increase in resistance per original resistance at 0°C per temperature change.

Ma'ana: Ƙaruwar juriya a kowane juriya na asali a 0°C a kowane canjin zafin jiki.

α = (R₁ - R₀) / [R₀ × (θ₁ - θ₀)]

R_θ = R₀ (1 + αθ)

Example: Temperature Effect on Resistance

Misali: Tasirin Zafin Jiki akan Juriya

A coil has resistance of 50Ω at 0°C. If α = 0.0043/°C, find resistance at 25°C.

Coil yana da juriya 50Ω a 0°C. Idan α = 0.0043/°C, nemo juriya a 25°C.

Step 1: Apply formula: R_θ = R₀ (1 + αθ)

Mataki na 1: Aiwatar dabara: R_θ = R₀ (1 + αθ)

Step 2: Calculate: R₂₅ = 50 × (1 + 0.0043 × 25) = 50 × (1 + 0.1075) = 50 × 1.1075 = 55.375Ω

Mataki na 2: Lissafa: R₂₅ = 50 × (1 + 0.0043 × 25) = 50 × (1 + 0.1075) = 50 × 1.1075 = 55.375Ω

Kirchhoff's Laws

Dokokin Kirchhoff

Kirchhoff's Current Law (KCL)

Dokar Halin Yanzu ta Kirchhoff (KCL)

The algebraic sum of currents entering a node is zero
Sum of currents entering = Sum of currents leaving
Based on conservation of charge

Jimlar aljebra na halin yanzu da ke shiga wani kulli sifili ne
Jimlar halin yanzu da ke shiga = Jimlar halin yanzu da ke fita
Ya dogara ne akan kiyaye caji

Kirchhoff's Voltage Law (KVL)

Dokar Ƙarfin Lantarki ta Kirchhoff (KVL)

The algebraic sum of voltages in any closed loop is zero
Sum of EMFs = Sum of voltage drops
Based on conservation of energy

Jimlar aljebra na ƙarfin lantarki a kowane madauki sifili ne
Jimlar EMFs = Jimlar raguwar ƙarfin lantarki
Ya dogara ne akan kiyaye makamashi

Exam Tip: When applying KVL, follow a consistent direction (clockwise or anticlockwise) and assign proper signs to voltage sources and drops.

Shawarar Jarrabawa: Lokacin amfani da KVL, bi hanya mai daidaito (agogo ko kuma akasin agogo) kuma sanya alamomin da suka dace ga tushen ƙarfin lantarki da raguwa.

Electrostatics and Capacitance

Lantarki Mai Tsayi da Ƙarfin Ƙwaƙwalwa

Coulomb's Law: The force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Dokar Coulomb: Ƙarfin da ke tsakanin caji biyu yana daidai da samfurin cajinsu kuma yana saba wa murabba'in nisa tsakaninsu.

F = k × (Q₁ × Q₂) / d²

where k = 9 × 10⁹ N·m²/C² (in vacuum)

Capacitance: The ability of a capacitor to store electric charge.

Ƙarfin Ƙwaƙwalwa: Ƙarfin capacitor na adana cajin lantarki.

C = Q / V

Energy stored: W = ½ C V²

Capacitor Connections

Haɗin Capacitor

Series: 1/C_eq = 1/C₁ + 1/C₂ + 1/C₃ + ...
Parallel: C_eq = C₁ + C₂ + C₃ + ...

Jere: 1/C_eq = 1/C₁ + 1/C₂ + 1/C₃ + ...
Kusa: C_eq = C₁ + C₂ + C₃ + ...

SI Prefixes

Gaban SI

Prefix	Gaban	Symbol	Multiplier
Tera	Tera	T	10¹²
Giga	Giga	G	10⁹
Mega	Mega	M	10⁶
Kilo	Kilo	k	10³
Milli	Mili	m	10⁻³
Micro	Mikro	μ	10⁻⁶
Nano	Nano	n	10⁻⁹
Pico	Piko	p	10⁻¹²

Exam Preparation Tips

Shawarwari don Shirye-shiryen Jarrabawa

Practice solving problems from both lecture notes and tutorials
Understand the concepts rather than memorizing formulas
Pay attention to units and ensure consistency in calculations
Review circuit analysis methods (Ohm's Law, Kirchhoff's Laws)
Practice with different circuit configurations (series, parallel, combination)
Understand the physical meaning of electrical parameters

Yi aiki kan warware matsaloli daga bayanan lacca da kuma darussan
Fahimci ra'ayoyin maimakon haddace dabaru
Kula da raka'a kuma tabbatar da daidaito a cikin lissafi
Bita hanyoyin bincike na da'ira (Dokar Ohm, Dokokin Kirchhoff)
Yi aiki tare da siffofin da'ira daban-daban (jere, kusa, haɗuwa)
Fahimci ma'anar jiki na ma'auni na lantarki

Good luck with your exams! Remember to practice regularly and understand the fundamental concepts.

Buri da kyau a jarrabawarku! Ku tuna yin aiki akai-akai kuma ku fahimci tushen ra'ayoyin.

Department of Computer Engineering - Katsina State Institute of Technology and Management

Reference: generated with "Deepseek AI" by Engineer Na'eem Auwal

EEC115