Current Electricity – Notes

1. Introduction

Current electricity is the flow of electric charge through a conductor. It is caused by the movement of electrons in a conductor like a wire.

Swahili: Umeme wa sasa ni mtiririko wa chaji za umeme kupitia kioo cha conductor. Hutokana na mwendo wa electrons ndani ya conductor kama waya.

2. Electric Current (I)

Electric current is the rate of flow of charge. It is measured in Amperes (A).

I = Q / t

• I = Current (Amperes, A)
• Q = Charge (Coulombs, C)
• t = Time (seconds, s)

3. Types of Current

• Direct Current (DC): Current flows in one direction only (e.g., battery).
• Alternating Current (AC): Current changes direction periodically (e.g., mains electricity).

4. Ohm's Law

Ohm's law states that the current through a conductor is directly proportional to the potential difference across it, provided the temperature remains constant.

V = I × R

• V = Voltage (Volts, V)
• I = Current (Amperes, A)
• R = Resistance (Ohms, Ω)

5. Resistance (R)

Resistance is the opposition to the flow of current. Depends on material, length, area, and temperature.

R = ρ × (L / A)

• ρ = Resistivity of material (Ω·m)
• L = Length of conductor (m)
• A = Cross-sectional area (m²)

6. Factors Affecting Resistance

• Material of conductor
• Length of conductor (longer → higher resistance)
• Cross-sectional area (thicker → lower resistance)
• Temperature (higher temperature → higher resistance in metals)

7. Electric Power (P)

Power is the rate at which electrical energy is consumed or produced.

P = V × I

Other forms:

P = I² × R

P = V² / R

8. Energy Consumed

Energy consumed by an electrical device is given by:

E = P × t

• E = Energy (Joules, J)
• P = Power (Watts, W)
• t = Time (seconds, s)

9. Combination of Resistors

Series Connection

Resistors are connected end-to-end.

R_total = R₁ + R₂ + R₃ + ...

Parallel Connection

Resistors are connected across the same potential difference.

1 / R_total = 1 / R₁ + 1 / R₂ + 1 / R₃ + ...

10. Kirchhoff’s Laws

Kirchhoff’s Current Law (KCL)

Sum of currents entering a junction = Sum of currents leaving the junction.

Kirchhoff’s Voltage Law (KVL)

Sum of EMF in a closed loop = Sum of potential drops in that loop.

11. EMF and Internal Resistance

Electromotive force (EMF) is the total energy supplied by a source per unit charge.

V = E – I·r

• V = Terminal voltage
• E = EMF of source
• I = Current
• r = Internal resistance

12. Practical Examples

• Calculating current in a simple circuit using Ohm’s law
• Determining energy consumed by a bulb
• Finding total resistance in series and parallel circuits

13. Circuit Diagrams

Battery (V) ──[Resistor R]─── Lamp
      |
      └───────────────────────

Series Circuit:
  ┌──R1───R2───R3───┐
  │                 │
  └────Battery──────┘

Parallel Circuit:
  ┌──R1──┐
  │      │
  │      └──R2──┐
  │             │
Battery─────────┘

14. Summary of Important Formulas

• Current: I = Q / t
• Ohm’s Law: V = I × R
• Resistance: R = ρ × L / A
• Power: P = V × I = I² × R = V² / R
• Energy: E = P × t
• Series: R_total = R₁ + R₂ + R₃
• Parallel: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃
• EMF & internal resistance: V = E – I·r