This chapter introduces the quantities, laws, and components that form the foundation of electrical engineering. The aim is to build an intuitive understanding before moving on to semiconductor physics and transistor circuits.
Learning Objectives
After completing this chapter, you should be able to:- distinguish between voltage, current, resistance, power, and energy;
- apply Ohm’s law to simple circuits;
- analyze series and parallel networks;
- use Kirchhoff’s current and voltage laws;
- calculate electrical power and energy;
- describe the basic behavior of capacitors and inductors;
- identify the most important properties of direct and alternating current.
1. Electric Charge, Current, and Voltage
Electric Charge
Electric charge is a fundamental property of matter. It is measured in coulombs (C). Electrons carry negative elementary charge, while protons carry positive elementary charge. The magnitude of the elementary charge is approximately \(1.602\times10^{-19}\,\mathrm{C}\).Electric Current
Electric current describes the rate at which charge passes through a cross-section of a conductor:\[I=\frac{\Delta Q}{\Delta t}\]
Current is measured in amperes (A), where one ampere corresponds to one coulomb per second. Conventional current is defined in the direction in which positive charge would move; electron flow in a metal is therefore opposite to the conventional current direction.
Voltage
Voltage is the difference in electric potential between two points. It describes the energy transferred per unit charge:\[V=\frac{\Delta W}{\Delta Q}\]
Voltage is measured in volts (V). A voltage can exist without current, but a sustained current requires a closed conducting path.
2. Resistance and Ohm’s Law
Electrical resistance opposes the flow of current. For an ohmic component at constant temperature, voltage and current are related by Ohm’s law:\[V=IR\]
Resistance is measured in ohms (Ω). The equation can also be written as \(I=V/R\) or \(R=V/I\).
For a uniform conductor, resistance depends on its material and geometry:
\[R=\rho\frac{l}{A}\]
Here, ρ is the resistivity of the material, l is the conductor length, and A is its cross-sectional area. Longer conductors have higher resistance, while a larger cross-section reduces resistance.
Example
A 1 kΩ resistor connected to a 5 V source carries:\[I=\frac{5\,\mathrm{V}}{1000\,\Omega}=5\,\mathrm{mA}\]
3. Series and Parallel Circuits
Resistors in Series
The same current flows through all components connected in series. The equivalent resistance is the sum of the individual resistances:\[R_{\mathrm{eq}}=R_1+R_2+\cdots+R_n\]
The source voltage is divided among the resistors. For two resistors, the voltage across R2 is:
\[V_2=V_{\mathrm{in}}\frac{R_2}{R_1+R_2}\]
Resistors in Parallel
Components connected in parallel share the same voltage. The total current is the sum of the branch currents:\[\frac{1}{R_{\mathrm{eq}}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots+\frac{1}{R_n}\]
For two parallel resistors:
\[R_{\mathrm{eq}}=\frac{R_1R_2}{R_1+R_2}\]
4. Kirchhoff’s Laws
Kirchhoff’s Current Law (KCL)
The algebraic sum of currents at a circuit node is zero. In other words, the total current entering a node equals the total current leaving it:\[\sum I=0\]
KCL follows from conservation of electric charge.
Kirchhoff’s Voltage Law (KVL)
The algebraic sum of all voltage rises and drops around a closed loop is zero:\[\sum V=0\]
KVL follows from conservation of energy. Together with Ohm’s law, KCL and KVL can be used to analyze a large class of linear circuits.
5. Electrical Power and Energy
Electrical power is the rate at which electrical energy is transferred or converted:\[P=VI\]
For a resistor, substitution of Ohm’s law gives two useful forms:
\[P=I^2R\qquad\text{and}\qquad P=\frac{V^2}{R}\]
Power is measured in watts (W). Electrical energy is power integrated over time. For constant power:
\[E=Pt\]
Energy is measured in joules (J), although kilowatt-hours (kWh) are commonly used for electrical consumption.
6. Capacitors
A capacitor stores energy in an electric field. Its capacitance is defined by:\[C=\frac{Q}{V}\]
Capacitance is measured in farads (F). The current-voltage relationship is:
\[i(t)=C\frac{dv(t)}{dt}\]
An ideal capacitor resists an instantaneous change in voltage. In a DC circuit it charges during a transient process and then behaves like an open circuit in steady state. The energy stored in a capacitor is:
\[E_C=\frac{1}{2}CV^2\]
For a resistor-capacitor circuit, the time constant is \(\tau=RC\). After one time constant, a charging capacitor has reached approximately 63.2% of its final voltage.
7. Inductors
An inductor stores energy in a magnetic field. Its voltage-current relationship is:\[v(t)=L\frac{di(t)}{dt}\]
Inductance is measured in henries (H). An ideal inductor resists an instantaneous change in current. In DC steady state, an ideal inductor behaves like a short circuit. The stored energy is:
\[E_L=\frac{1}{2}LI^2\]
For a resistor-inductor circuit, the time constant is \(\tau=L/R\).
8. Direct and Alternating Current
Direct Current (DC)
Direct current maintains a constant polarity. Batteries and regulated power supplies are typical DC sources. A DC voltage may vary in magnitude, but it does not periodically reverse polarity.Alternating Current (AC)
Alternating current changes magnitude and direction with time. A sinusoidal voltage can be written as:\[v(t)=V_{\mathrm{peak}}\sin(2\pi ft+\varphi)\]
Here, f is the frequency and φ is the phase angle. For a sine wave:
\[V_{\mathrm{RMS}}=\frac{V_{\mathrm{peak}}}{\sqrt{2}}\]
RMS values are useful because they express the equivalent heating effect of an AC signal in a resistor.
9. Component Overview
| Component | Main Function | Stored Energy |
|---|---|---|
| Resistor | Limits current and dissipates energy | None in the ideal model |
| Capacitor | Opposes rapid voltage changes | Electric field |
| Inductor | Opposes rapid current changes | Magnetic field |
| Diode | Conducts primarily in one direction | Not an energy-storage component |
| Transistor | Switches or amplifies electrical signals | Not an energy-storage component |
10. A Systematic Method for Circuit Analysis
- Draw a clear circuit diagram and define voltage polarities and current directions.
- Identify series and parallel combinations that can be simplified.
- Apply Ohm’s law and the component equations.
- Write KCL equations for important nodes and KVL equations for independent loops.
- Solve the equations with consistent units.
- Check whether the sign, magnitude, and power balance of the result are physically plausible.