Electric Charge
Electric charge is a basic property of matter due to which it experiences a force when placed in an electric field. Electric charge is represented by q. There are two types of charge: positive and negative. Positive and negative charges attract each other, while charges of the same type repel each other.
Charge Fundamentals
- Unit of charge: Coulomb (C)
- Fundamental charge: Electron charge = \(1.6 \times 10^{-19}\) C
Electric Current Formula
\[ i = \frac{q}{t} \]Where: i = current (amperes), q = charge (coulombs), t = time (seconds)
Key Points:
- Definition of quantity of charge and current, their units of measurement
- Direction of current is opposite to the flow of electrons
- Current is measured with an ammeter
Introduction to Potential Difference (Voltage)
Potential Difference Formula
\[ V = \frac{W}{q} \]Where: V = potential difference (volts), W = work (joules), q = charge (coulombs)
Important Concept
An electric cell or battery provides potential difference. When there is a conductor between the positive and negative terminals of a cell, electrons flow from lower potential to higher potential. The direction of current is opposite to that of electron flow.
Potential difference represents the energy required to move a charge between two points. It is measured by a voltmeter.
Resistance and Resistivity
Resistance Formula
\[ R = \rho \frac{l}{A} \]Where: R = resistance (ohms), ρ = resistivity (Ω·m), l = length (m), A = cross-sectional area (m²)
Key Properties:
- Resistance increases directly with length
- Resistance decreases inversely with cross-sectional area
- Resistivity is a material property measured in ohm-meters (Ω·m)
Circuit Combinations: Series and Parallel
Series Circuit
Current same throughout
\[ R_{eq} = R_1 + R_2 + R_3 + \cdots \]
Parallel Circuit
Voltage same across all
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots \]
Key Differences:
- In series: Current same, voltage divided
- In parallel: Voltage same, current divided
- Total parallel resistance is less than smallest resistor
Ohm's Law and Applications
Ohm's Law Formula
\[ V = IR \]Where: V = voltage (volts), I = current (amperes), R = resistance (ohms)
Ohm's Law Statement
"If the temperature is constant, the potential difference between the two ends of a conductor is proportional to the current."
Ohm's Law shows the relationship between current, voltage, and resistance. The graph of voltage vs current is a straight line through the origin.
Electric Power and Energy
Power Formulas
\[ P = VI = I^2 R = \frac{V^2}{R} \]Where: P = power (watts)
Energy Formula
\[ E = P \times t \]Where: E = energy (kilowatt-hour), t = time (hours)
Key Points:
- 1 kilowatt-hour = \(3.6 \times 10^6\) joules
- Electric energy is measured by electricity meters
- Electric bills are calculated based on kilowatt-hour consumption
Heating Effect and Joule's Law
Joule's Law of Heating
\[ H = I^{2} R t \]Where: H = heat generated (joules)
Practical Applications
The heating effect of electric current is utilized in:
- Electric heaters
- Electric irons
- Toasters
- Electric kettles
Safety Devices: Electric Fuse
Fuse Characteristics
- High resistivity alloy
- Low melting point
- Connected in series with the circuit
- Must be correctly rated for the circuit
The fuse wire heats up and melts when excessive current flows through it, breaking the circuit and protecting electrical devices.
Practical Examples and Calculations
Sample Problems:
- Calculate the current when 20C of charge flows through a conductor in 4 seconds.
- Find the resistance of a 10m long copper wire with 2mm diameter (ρ = 1.7 × 10⁻⁸ Ω·m).
- Determine the equivalent resistance of three 6Ω resistors in parallel.
- Calculate the energy consumed by a 100W bulb in 5 hours.
Conclusion
This chapter provides a comprehensive knowledge of electricity from basic principles to complex electrical circuits and their connections. The scientific analysis and calculation formulas of the major elements like charge, current, potential difference, resistance, and electric power are clearly presented.
The practical application of this knowledge is essential in the proper operation and safety of electrical equipment. This in-depth study of electricity will not only enable students to achieve academic success but also prepare them for the safe and effective use of electricity in the modern technological age.
Summary of Key Points
- Charge (q): Positive and negative, unit coulomb
- Current (i): Flow of charge, formula \(i = \frac{q}{t}\), unit ampere
- Potential Difference (V): Work done per charge, formula \(V = \frac{W}{q}\), unit volt
- Resistance (R): Resistance to current, formula \(R = \rho \frac{l}{A}\), unit ohm
- Ohm's Law: \(V = IR\), ratio of potential difference and current
- Series and Parallel Combination: Laws of distribution of current and voltage
- Electric Power (P): \(P = VI\), rate of energy
- Heating Effect: \(H = I^2 Rt\), heat generated due to current
- Fuse: Safety device, melts at high current
- Electrical Energy: \(E = Pt\), unit kilowatt-hour, used in calculating electricity bill