Bachelors Program in Electronics and Communication
Basic Electronics
•
Bachelor
Electrical and Electronic Foundations
Introduction
Electrical engineering describes how charge moves, how energy is transferred, and how interconnected components constrain voltage and current. These ideas support later study of semiconductor devices, amplifiers, communication systems, digital electronics, instrumentation, and embedded systems.
Circuit theory is an abstraction. A physical circuit is represented by components connected through idealized nodes and branches. This lumped-element model is accurate when component dimensions are much smaller than the wavelength of relevant electromagnetic signals and when propagation delay, radiation, and distributed electromagnetic effects are negligible. At sufficiently high frequencies, transmission-line and electromagnetic-field models become necessary.
Learning Objectives
After studying this chapter, students should be able to:
explain charge, current, voltage, power, and energy;
use SI units and engineering prefixes correctly;
distinguish common signal classifications;
model resistors, capacitors, inductors, and practical sources;
apply the passive sign convention;
explain reference, chassis, and protective-earth grounds;
apply Ohm’s law and Kirchhoff’s laws to DC circuits;
calculate component power and stored energy;
select safe, appropriate measurement practices; and
recognize the limitations of elementary circuit models.
1. Electric Charge and Current
1.1 Electric charge
Electric charge is a fundamental property of matter. Its SI unit is the coulomb (C). Charge occurs in integer multiples of the elementary charge magnitude e = 1.602 × 10-19 C. A proton carries +e, while an electron carries -e.
For an integer number of elementary charges,
Q = N e
where Q is charge in coulombs, N is the signed number of elementary charges, and e is the elementary charge magnitude. In macroscopic circuit calculations, charge is usually treated as continuous because the number of carriers is extremely large.
Charge is conserved: it cannot be created or destroyed in an isolated system, although positive and negative charges may be separated or recombined.
1.2 Electric current
Current is the rate at which charge crosses a specified surface:
i(t) = \frac{dq(t)}{dt}
Here i(t) is instantaneous current in amperes (A), q(t) is net charge in coulombs, and t is time in seconds. Thus, 1 A = 1 C/s. Over a time interval,
q(t2)-q(t1)=\intt1t2 i(t)\,dt
Conventional current is defined in the direction of positive-charge motion. In a metal, electrons usually drift in the opposite direction. This convention does not affect circuit calculations if current reference directions are used consistently.
Example: charge transfer. If a steady current of 250 mA flows for 40 s, then
Q = It = (0.250\ A)(40\ s)=10\ C
The magnitude of the number of electrons involved is approximately 10/(1.602 × 10-19) = 6.24 × 1019.
2. Voltage, Power, and Energy
2.1 Voltage
Voltage is electric potential difference: the work or energy transferred per unit charge between two points.
vab=\frac{dw}{dq}
In this expression, vab is the voltage of point a relative to point b in volts, w is energy in joules, and q is charge in coulombs. Therefore, 1 V = 1 J/C. Voltage always refers to two points, even when one point is implicitly designated as the circuit reference.
2.2 Passive sign convention
Under the passive sign convention, the referenced current enters the terminal marked positive for the referenced voltage. The instantaneous power absorbed by the element is then
p(t)=v(t)i(t)
Positive p means that the element absorbs energy. Negative p means that it delivers energy to the rest of the circuit. This interpretation depends on the selected voltage polarity and current direction.
Electrical energy transferred from time t1 to t2 is
W=\intt1t2p(t)\,dt=\intt1t2v(t)i(t)\,dt
Power is measured in watts (W), where 1 W = 1 J/s. Energy is measured in joules (J), although electricity billing commonly uses the kilowatt-hour:
1\ kWh = 3.6 × 106\ J
Example: load energy. A 12 V load drawing 0.50 A absorbs P=(12)(0.50)=6.0 W. If it operates for 30 min, or 1800 s, its energy consumption is W=(6.0)(1800)=10.8 kJ, equivalent to 0.003 kWh.
3. SI Units and Engineering Notation
Using consistent units prevents calculation errors. Common quantities are summarized below.
Quantity
Symbol
SI unit
Unit symbol
Charge
Q or q
coulomb
C
Current
I or i
ampere
A
Voltage
V or v
volt
V
Resistance
R
ohm
Ω
Capacitance
C
farad
F
Inductance
L
henry
H
Power
P or p
watt
W
Energy
W or E
joule
J
Frequency
f
hertz
Hz
Uppercase symbols commonly represent constant or DC values, while lowercase symbols often represent time-varying quantities. This is a convention rather than a universal rule.
Prefix
Symbol
Factor
giga
G
109
mega
M
106
kilo
k
103
milli
m
10-3
micro
μ
10-6
nano
n
10-9
pico
p
10-12
Prefix symbols are case-sensitive: 1 mW is one milliwatt, whereas 1 MW is one megawatt. Good engineering practice includes writing units with every intermediate numerical result and checking dimensional consistency.
4. Electrical Signals
A signal is a voltage, current, or other measurable quantity that conveys information or describes system behavior.
4.1 Signal classifications
DC signal: constant with time under the ideal definition.
Time-varying signal: changes with time.
Periodic signal: repeats after a period T, so x(t+T)=x(t).
Aperiodic signal: has no finite repeating period.
Analog signal: continuous in amplitude over its defined range.
Digital signal: represented using a finite set of nominal levels or symbols.
Deterministic signal: describable by a known mathematical rule.
Random signal: requires probabilistic description.
A sinusoidal voltage can be written as
v(t)=Vm\sin(ωt+φ)
where Vm is peak amplitude in volts, ω is angular frequency in radians per second, and φ is phase in radians. Frequency and period satisfy
f=\frac{1}{T}, \qquad ω=2πf
For a periodic signal, its root-mean-square value is
Xrms=\sqrt{\frac{1}{T}\intt0t0+Tx2(t)\,dt}
This general expression applies to any square-integrable periodic waveform. For a zero-offset sinusoid only,
Vrms=\frac{Vm}{\sqrt{2}}
RMS values are important because a DC voltage equal to an AC voltage’s RMS value produces the same average heating in an ideal resistor.
Digitizing an analog signal requires sampling and quantization. For an ideally band-limited signal with highest frequency fmax, unique theoretical reconstruction requires a sampling frequency greater than 2fmax. Practical systems use higher rates and anti-aliasing filters because physical filters are non-ideal and real signals are not perfectly band-limited.
5. Passive Circuit Components
5.1 Resistor
An ideal linear resistor obeys Ohm’s law:
v(t)=Ri(t)
Here R is constant resistance in ohms, and voltage and current follow the passive sign convention. This relation is a component model, not a universal law for every device. Diodes, lamps, thermistors, and transistors can have nonlinear or condition-dependent voltage–current relationships.
The power absorbed by a positive resistance is
p=vi=i2R=\frac{v2}{R}
The last two forms follow from Ohm’s law and apply to an ideal linear resistor. Real resistors have tolerances, temperature coefficients, voltage limits, and maximum power ratings.
5.2 Capacitor
An ideal capacitor stores separated charge. For a constant capacitance,
q(t)=Cv(t), \qquad i(t)=C\frac{dv(t)}{dt}
Capacitance C is measured in farads. Integrating the current relation gives
v(t2)-v(t1)=\frac{1}{C}\intt1t2i(t)\,dt
Consequently, a finite, non-impulsive capacitor current cannot produce an instantaneous voltage change over a zero-duration interval. However, an ideal current impulse with finite area ∆Q=\int i(t)dt can produce a voltage jump ∆v=∆Q/C. This distinction is essential in idealized transient analysis.
The stored energy is
WC=\frac{1}{2}Cv2
This formula assumes an ideal linear capacitor and uses the instantaneous voltage magnitude across it.
5.3 Inductor
An ideal linear inductor satisfies
v(t)=L\frac{di(t)}{dt}
Inductance L is measured in henrys. Its current change is
i(t2)-i(t1)=\frac{1}{L}\intt1t2v(t)\,dt
A finite, non-impulsive voltage cannot instantaneously change ideal-inductor current. An ideal voltage impulse of finite time integral can cause a current jump. The stored magnetic energy is
WL=\frac{1}{2}Li2
Real capacitors and inductors include losses, leakage, parasitic resistance, and frequency-dependent behavior. Their ideal models are useful only within specified operating ranges.
6. Independent and Dependent Sources
An ideal voltage source maintains its specified voltage regardless of current. An ideal current source maintains its specified current regardless of terminal voltage. These models can deliver unlimited power under certain connections and therefore cannot be physically realized over unrestricted operating ranges.
A practical voltage source is often approximated by an ideal voltage source in series with an internal resistance. Its terminal voltage decreases as load current increases:
VL=Vs-ILRs
Here Vs is the open-circuit source voltage, Rs is series resistance, and VL is loaded terminal voltage. A practical current source may be modeled as an ideal current source in parallel with a finite output resistance.
Dependent sources have values controlled by another circuit voltage or current. They are necessary for transistor, amplifier, and feedback models. A dependent source can deliver power, but its energy ultimately comes from the modeled physical device’s power supply.
7. Nodes, Branches, Loops, and Ground
A node joins two or more component terminals. All points connected by ideal wire belong to the same node and have the same modeled potential. A branch is a two-terminal path carrying one branch current. A loop is a closed path through the circuit.
Single-loop circuit containing an independent voltage source and a resistor
Figure: Single-loop circuit containing an independent voltage source and a resistor
Figure: A correctly connected single-loop circuit. The source, resistor, and conductors form one series path without a short circuit.
The word ground has several meanings:
Circuit reference or signal ground: the node assigned 0 V for analysis.
Protective earth: a safety connection to the Earth, intended to conduct fault current.
Chassis ground: connection to a conductive enclosure.
Virtual ground: a node maintained near a reference potential by active circuitry but not necessarily able to absorb arbitrary current.
These grounds are not automatically interchangeable. A battery-powered circuit reference may have no physical Earth connection. Incorrect grounding can create shock hazards, noise, ground loops, or damage through unintended current paths.
8. Kirchhoff’s and Ohm’s Laws
8.1 Kirchhoff’s current law
Kirchhoff’s current law (KCL) follows from charge conservation. For a lumped node with negligible net charge accumulation,
\sumk=1n ik=0
Currents entering and leaving must be assigned consistent signs. An equivalent statement is that the sum of currents entering a node equals the sum leaving it. Capacitor currents are included as branch currents where applicable.
8.2 Kirchhoff’s voltage law
Kirchhoff’s voltage law (KVL) states that the algebraic sum of branch voltages around a closed lumped-circuit loop is zero:
\sumk=1nvk=0
KVL reflects energy conservation when electromagnetic induction is either negligible or represented explicitly by circuit elements. If a time-varying magnetic flux links a physical loop, Faraday’s law must be considered; applying elementary KVL without accounting for the induced electromotive force can be misleading.
For the series circuit in the figure, KVL gives
Vs-IR=0
and therefore I=Vs/R.
8.3 Series and parallel resistance
Resistors are in series only when the same current must flow through each without branching at their shared nodes:
Req=R1+R2+\cdots+Rn
Resistors are in parallel when they share the same two nodes and therefore have the same voltage:
For two positive resistors in parallel, the special-case expression is Req=R1R2/(R1+R2).
8.4 Worked circuit analysis
A 12 V source supplies a 2 kΩ resistor in series with a parallel combination of 3 kΩ and 6 kΩ.
First, combine the parallel resistors:
Rp=\frac{(3\ kΩ)(6\ kΩ)}{3\ kΩ+6\ kΩ}=2\ kΩ
The total resistance is RT=2 kΩ+2 kΩ=4 kΩ, so the source current is
Is=\frac{12\ V}{4\ kΩ}=3\ mA
The voltage across the parallel network is Vp=(3 mA)(2 kΩ)=6 V. Branch currents are
I1=\frac{6\ V}{3\ kΩ}=2\ mA, \qquad I2=\frac{6\ V}{6\ kΩ}=1\ mA
KCL is satisfied because 3 mA=2 mA+1 mA. The source delivers 36 mW. The resistors absorb 18 mW, 12 mW, and 6 mW respectively, totaling 36 mW and confirming power conservation.
9. Measurement and Laboratory Practice
A voltmeter is connected in parallel with the points whose voltage is required. An ideal voltmeter has infinite input resistance; a real meter has high but finite input resistance and can load high-resistance circuits.
An ammeter is inserted in series with the measured branch. An ideal ammeter has zero resistance; a real ammeter introduces a small burden voltage. Connecting an ammeter directly across a voltage source can cause excessive current, equipment damage, or injury.
An oscilloscope displays time-varying voltage. On many bench oscilloscopes, the probe ground clip is connected to protective earth. Attaching it to a non-ground circuit node can create an unintended short circuit. Differential probes or isolated instruments are required in some floating or high-voltage measurements.
Best practice includes:
de-energizing circuits before changing connections;
checking instrument category and voltage ratings;
beginning with a safe measurement range;
verifying polarity and reference nodes;
accounting for probe loading and bandwidth;
using current-limited supplies during initial testing; and
documenting assumptions, tolerances, and uncertainty.
10. Illustrative Case: Loading of a Sensor Output
Background
This fictional case concerns a sensor board specified to produce an open-circuit output of 5.0 V. The board is modeled explicitly by a 5.0 V ideal source in series with an unknown output resistance Rs. A controller input is represented by a 2.0 kΩ load resistor connected from the sensor output node to the common reference ground. The loaded output voltage is measured as 3.8 V.
Problem
Determine the sensor’s equivalent series resistance and assess whether the controller input is loading the sensor significantly.
Analysis
The topology is a series path consisting of the 5.0 V source, Rs, and the 2.0 kΩ load. The output voltage is measured across the load. Thus,
The voltage drop across the output resistance is 1.2 V, consistent with (1.90 mA)(631.6 Ω)=1.20 V. The load power is (3.8 V)(1.90 mA)=7.22 mW, while the series resistance dissipates approximately (1.90 mA)2(631.6 Ω)=2.28 mW.
Approach and Solution
Because the controller reduces the nominal output from 5.0 V to 3.8 V, the loading error is 24%. If the controller requires a voltage close to 5.0 V, an input with substantially higher resistance should be used. Alternatively, a suitable voltage buffer can isolate the sensor from the 2.0 kΩ load. Buffer input range, output-current capability, supply rails, offset, noise, and stability must all be checked.
Outcome
The inferred sensor output resistance is approximately 632 Ω. The clearly specified series-source and shunt-load topology shows that the observed voltage reduction is caused by voltage division rather than an unexplained sensor fault.
Learning Points
Measuring a source requires considering both source and instrument impedances.
An open-circuit voltage does not guarantee the same voltage under load.
Circuit topology must be stated before numerical inference.
Power and signal-integrity checks should accompany voltage calculations.
11. Model Limitations and Contemporary Practice
Elementary circuit theory assumes ideal wires and lumped components. Real interconnects possess resistance, capacitance, inductance, propagation delay, and electromagnetic coupling. Component values also vary with manufacturing tolerance, temperature, age, voltage, frequency, and mechanical stress.
At high frequencies, a conductor may behave as a transmission line rather than an equipotential node. Fast digital edges contain high-frequency spectral components even when the clock frequency is modest. Consequently, grounding, return-current paths, impedance control, shielding, and electromagnetic compatibility become central design concerns.
Modern electronic design uses circuit simulation, automated measurement, and AI-assisted diagnostic tools. These tools can identify patterns and accelerate design exploration, but their models and generated recommendations must be checked against physical laws, component ratings, measurement uncertainty, and safety requirements. Simulation does not replace verification on representative hardware.
Engineers also have ethical and regulatory responsibilities. Products must protect users from electric shock, excessive temperature, fire, electromagnetic interference, and foreseeable misuse. Responsible practice includes truthful specification, traceable testing, safe disposal of batteries and electronic waste, and compliance with applicable electrical safety and electromagnetic-compatibility standards.
Chapter Summary
Charge is measured in coulombs, and current is its rate of flow. Voltage represents energy transferred per unit charge. Power is the rate of energy transfer and is interpreted using defined voltage polarity, current direction, and the passive sign convention.
Resistors dissipate energy, while ideal capacitors and inductors store electric and magnetic energy. A finite, non-impulsive current cannot instantaneously change ideal-capacitor voltage, although a current impulse of finite area can. The corresponding dual statement applies to ideal-inductor current and voltage impulses.
Ohm’s law describes ideal linear resistors. KCL follows from charge conservation, while KVL applies to lumped loops when electromagnetic induction is negligible or properly represented. Practical sources have finite output impedance, so connected loads can alter terminal voltage. Reliable engineering therefore requires explicit topology, consistent SI units, awareness of model limitations, safe grounding, and correct measurement methods.
Key Terms
Charge: Fundamental electrical property measured in coulombs.
Current: Rate at which charge crosses a surface.
Voltage: Electric potential difference or energy transferred per unit charge.
Power: Rate of electrical energy transfer.
Energy: Capacity transferred or stored, measured in joules.
Passive sign convention: Reference convention in which current enters an element’s positive-voltage terminal.
Signal: A measurable quantity that varies to represent information or system behavior.
RMS value: Effective magnitude based on the square root of the mean squared waveform.
Resistance: Opposition characterized for an ideal resistor by the ratio of voltage to current.
Capacitance: Charge-storage property relating capacitor charge and voltage.
Inductance: Magnetic energy-storage property relating voltage to current rate of change.
Node: Set of ideal-conductor points at the same potential.
Branch: Two-terminal circuit path carrying a branch current.
Loop: Closed path through a circuit.
Ground: A reference, safety, or chassis connection whose meaning depends on context.
Ohm’s law: Linear resistor relation v=Ri.
Kirchhoff’s current law: Algebraic sum of currents at a lumped node is zero.
Kirchhoff’s voltage law: Algebraic sum of voltages around an applicable lumped loop is zero.
Review Questions
Short Answer Questions
Define conventional current and explain its relation to electron motion in a metal.
What does positive power mean under the passive sign convention?
Distinguish circuit-reference ground from protective earth.
State the conditions defining series and parallel resistors.
Why can a real voltmeter alter the voltage being measured?
Long Answer Questions
Derive the resistor power relations from Ohm’s law and discuss their applicability.
Explain capacitor and inductor continuity properties, including the effect of ideal impulses.
Discuss the physical foundations and limitations of KCL and KVL.
Compare ideal and practical voltage and current sources.
Explain how signal frequency, RMS value, sampling, and aliasing influence electronic measurement.
Analytical / Application Questions
A 24 V source supplies 1 kΩ and 2 kΩ resistors in series. Calculate current, each voltage drop, and each resistor’s power.
A 10 V source with 200 Ω series resistance supplies an 800 Ω load. Determine load voltage, current, and source-resistance power loss.
A 20 μF capacitor initially at 2 V receives a current pulse whose total charge is 60 μC. Using the ideal-capacitor model, determine the final voltage and state why this result permits an instantaneous change if the pulse is idealized as an impulse.
Multiple Choice Questions with Answers
Question 1
A constant current transfers 3.2 C of charge in 0.8 s. What is the current?
A. 0.25 A
B. 2.4 A
C. 4.0 A
D. 8.0 A
Correct Answer: C. 4.0 A
Question 2
A 12 V source is connected across a 4 kΩ resistor. What current flows?
A. 0.33 mA
B. 3.0 mA
C. 48 mA
D. 300 mA
Correct Answer: B. 3.0 mA
Question 3
Which statement about an ideal capacitor is correct?
A. Its voltage can never change instantaneously under any mathematical excitation.
B. A finite, non-impulsive current can change its voltage instantaneously.
C. A current impulse with finite area can cause an instantaneous voltage change.
D. Its current must always be zero in a time-varying circuit.
Correct Answer: C. A current impulse with finite area can cause an instantaneous voltage change.
Question 4
Under the passive sign convention, an element with v=8 V and i=2 A has current entering its positive terminal. What is its power behavior?
A. It absorbs 16 W.
B. It delivers 16 W.
C. It absorbs 4 W.
D. It stores exactly 16 J.
Correct Answer: A. It absorbs 16 W.
Question 5
What is the RMS value of a zero-offset sinusoidal voltage with a 10 V peak amplitude?
A. 5.00 V
B. 7.07 V
C. 10.0 V
D. 14.1 V
Correct Answer: B. 7.07 V
Question 6
A 5.0 V source with unknown series resistance supplies a 2.0 kΩ load. The measured load voltage is 3.8 V. What is the series resistance?
A. 158 Ω
B. 400 Ω
C. 632 Ω
D. 2.63 kΩ
Correct Answer: C. 632 Ω
Question 7
Which principle is the physical basis of Kirchhoff’s current law?
A. Conservation of charge
B. Conservation of momentum
C. Electromagnetic induction
D. Quantization of energy
Correct Answer: A. Conservation of charge
Question 8
How is a practical voltage source commonly modeled at low frequencies?
A. An ideal voltage source in parallel with zero resistance
B. An ideal voltage source in series with internal resistance
C. An ideal current source in series with infinite resistance
D. A capacitor connected without a source
Correct Answer: B. An ideal voltage source in series with internal resistance
Question 9
Which statement about circuit ground is correct?
A. Every circuit-reference ground is physically connected to Earth.
B. Ground always carries zero current.
C. Circuit reference, chassis ground, and protective earth may have different functions.
D. A virtual ground can absorb unlimited current.
Correct Answer: C. Circuit reference, chassis ground, and protective earth may have different functions.
Question 10
A 100 Ω resistor carries 20 mA. What power does it absorb?