Study guide
1.2 DC Circuits, Voltage, Current, and Ohm's Law
ACMA Amateur Radio Standard Recognition Certificate - Theory Exam
Track your progress as you read
Finished sections get a check mark.
1 Chapter 1: Electrical Principles and Components
1.1 Mathematics, Units and Metric Prefixes 1.2 DC Circuits, Voltage, Current, and Ohm's Law 1.3 Power, Energy, and Resistance Calculations 1.4 Resistor Colour Code and Component Symbol Identification 1.5 Capacitors: Construction, Ratings and Safety 1.6 Inductors: Construction, Factors Affecting Inductance and Combinations 1.7 Capacitor and Inductor Combination Calculations 1.8 AC Circuits, Frequency, Wavelength, and RMS Values 1.9 Reactance and Impedance in AC Circuits 1.10 Resonance, Q Factor and Tuned Circuits 1.11 Transformers: Turns Ratio, Impedance Matching and Eddy Currents 1.12 Rectifiers, PIV and Power Supply Smoothing 1.13 Active Components: Semiconductors, Diodes, and Transistors 1.14 Transistor and FET Symbols, Configurations and External Behaviour
2 Chapter 2: Transmitters and Receivers
2.1 Superheterodyne Receiver Architecture and Block Diagrams 2.2 Frequency Converters, IF Amplifiers and Transceiver Sharing 2.3 Receiver Performance: Sensitivity, Selectivity, and AGC 2.4 Signal-to-Noise Ratio and Receiver Noise Performance 2.5 Transmitter Architecture, Oscillators and Frequency Synthesisers 2.6 Transmission Quality: Frequency Drift, Parasitic Oscillation and Over-Modulation 2.7 Modulation Techniques: AM, FM, and SSB 2.8 Amplifier Classes and Power Amplifiers (Class A, B, C, and AB) 2.9 Modulation, Duty Cycle and Rated Transmitter Power 2.10 Transceiver Control: ALC, Squelch, and Digital Modes 2.11 Digital Transmission Modes and Bandwidth
3 Chapter 3: Transmission Lines and Antennas
3.1 Transmission Lines: Coaxial, Twin-Lead, and Characteristic Impedance 3.2 Standing Wave Ratio (SWR) and Reflection Loss 3.3 Impedance Matching, Baluns, and Antenna Tuning Units (ATUs) 3.4 Resonant Antennas: Dipoles, Verticals, and End-Fed Antennas 3.5 Angle of Radiation, Antenna Height and Current Distribution 3.6 Directional Antennas: Yagis, Gain and Radiation Patterns 3.7 Effective Radiated Power: System Gains and Losses
4 Chapter 4: Radio Wave Propagation
4.1 Electromagnetic Waves: Velocity, Wavelength and Polarisation 4.2 Ground Wave, Direct Wave and Line-of-Sight Propagation 4.3 Ionospheric Layers (D, E, F1, F2) and Skywave Propagation 4.4 Critical Frequency, Maximum Usable Frequency (MUF), and Fading 4.5 Solar Activity, Sunspot Cycles, and VHF Anomalous Propagation 4.6 Seasonal and Diurnal Effects on Band Selection
5 Chapter 5: Electrical and RF Measurements
5.1 Multimeter Operation: Voltage, Current, and Resistance Measurements 5.2 RF Power and SWR Measurement (PEP vs. Average Power) 5.3 Frequency Counters, Dummy Loads, and Test Equipment 5.4 Frequency Standards, Crystal Calibrators and Standard-Frequency Transmissions
6 Chapter 6: Interference and Electromagnetic Compatibility (EMC)
6.1 Harmonic Emissions, Spurious Signals, and Transmitter Filtering 6.2 How Interference Enters Television and Broadcast Receivers 6.3 Masthead Amplifier Overload and Audio-Stage Demodulation 6.4 Electromagnetic Interference (EMI), Breakthrough, Ferrites, and EMC 6.5 Filter Types, Response Curves and EMC Filter Selection 6.6 EMC Good Practice: Minimum Power, Balanced Antennas and Feedline Routing 6.7 Vehicle EMC and Resolving Community Interference Complaints
7 Chapter 7: Safety and Environmental Hazards
7.1 Mains Voltage Safety, Earthing, and High-Voltage Capacitors 7.2 Equipment Approval, Mains Wiring and Fuse Practice 7.3 Station Layout, Cabling and Emergency Shut-Off 7.4 Lightning Protection and Station Security 7.5 Electric Shock: Prevention, Rescue and Emergency Response 7.6 Battery, Chemical and Hearing Safety in the Amateur Station 7.7 RF Exposure: EMR Hazards and Safe Distance 7.8 Antenna Erection, Siting and Power Line Safety
1.2 DC Circuits, Voltage, Current, and Ohm's Law
Key Takeaways Explain This Topic AI
Direct Current (DC) flows in a single invariant direction from positive to negative potential in conventional current flow.
Ohm's Law establishes the fundamental linear mathematical relationship between potential difference (V in Volts), electric current (I in Amperes), and resistance (R in Ohms): V = I × R, I = V / R, and R = V / I.
In a series circuit, total resistance is the sum of all individual resistances (R_total = R1 + R2 + ... + Rn), and current remains identical through every component.
In a parallel circuit, the reciprocal of total resistance equals the sum of reciprocals of branch resistances (1/R_total = 1/R1 + 1/R2 + ... + 1/Rn), and potential difference across every branch is identical.
Kirchhoff's Current Law (KCL) states that the sum of currents entering any circuit node equals the sum leaving it; Kirchhoff's Voltage Law (KVL) states that the algebraic sum of voltages around any closed loop is zero.
Last updated: July 2026
1.2 DC Circuits, Voltage, Current, and Ohm's Law
Understanding direct current (DC) circuits is the bedrock of radio communications engineering and the starting point for the Australian Communications and Media Authority (ACMA) Standard Recognition Certificate examination. All electronic radio equipment—from low-noise preamplifiers and digital signal processors to high-power RF final amplifiers—relies on stable DC voltages and currents to bias active semiconductor components and establish operating parameters.
1. Electrical Fundamentals: Charge, Voltage, Current, and Resistance
At the subatomic level, electrical phenomena stem from the movement and interaction of charged subatomic particles. Electrons carry a negative elementary charge of approximately 1.602 × 10 − 19 1.602 \times 10^{-19} 1.602 × 1 0 − 19 Coulombs. In conductive materials, such as copper, silver, and aluminium, outer-shell valence electrons are loosely bound to atomic nuclei, forming a "sea" of free electrons capable of drifting through the crystal lattice when exposed to an electric field.
Potential Difference (Voltage, V V V )
Electric potential difference—commonly termed Voltage ( V V V ) or Electromotive Force (EMF) —is the force or pressure that drives free electrons through a conductor. Voltage represents the work required to move a unit charge between two points against an electric field. The SI unit of potential difference is the Volt (V) , named after Alessandro Volta. One Volt is defined as the potential difference across a conductor when a current of one Ampere dissipates one Watt of power ( 1 V = 1 J/C 1\text{ V} = 1\text{ J/C} 1 V = 1 J/C ).
In radio station equipment, DC operating voltages vary widely:
13.8 V DC 13.8\text{ V DC} 13.8 V DC : Standard nominal DC voltage for mobile and desktop transceiver power supplies (matching a charging 12V lead-acid or LiFePO 4 \text{LiFePO}_4 LiFePO 4 battery).
5.0 V 5.0\text{ V} 5.0 V & 3.3 V 3.3\text{ V} 3.3 V : Standard logic levels for microcontrollers, synthesisers, and DSP circuitry.
50 V 50\text{ V} 50 V - 3000 V DC 3000\text{ V DC} 3000 V DC : Anode/drain voltages found in high-power solid-state or vacuum tube RF linear amplifiers.
Electric Current ( I I I )
Current ( I I I ) is the rate of flow of electric charge past a specified point in a circuit. The SI unit of current is the Ampere (A) , named after André-Marie Ampère. One Ampere represents the flow of one Coulomb of charge ( 6.242 × 10 18 6.242 \times 10^{18} 6.242 × 1 0 18 electrons) passing a boundary per second ( 1 A = 1 C/s 1\text{ A} = 1\text{ C/s} 1 A = 1 C/s ).
In DC circuits, current flows in a single continuous direction. It is important for ACMA candidates to distinguish between two conventions:
Conventional Current Flow : Assumes positive charge moves from the positive terminal of a voltage source, through the external circuit, to the negative terminal. This convention is standard in circuit diagrams and mathematical calculations.
Electron Flow : Reflects the physical movement of negatively charged electrons, which travel from the negative terminal toward the positive terminal.
Common current metric prefixes in amateur radio include:
Microampere ( μ A \mu\text{A} μ A ): 10 − 6 A 10^{-6}\text{ A} 1 0 − 6 A (e.g., receiver AGC bias currents).
Milliampere ( mA \text{mA} mA ): 10 − 3 A 10^{-3}\text{ A} 1 0 − 3 A (e.g., small-signal transistor stage biasing).
Ampere ( A \text{A} A ): 10 0 A 10^{0}\text{ A} 1 0 0 A (e.g., transmit current drawn by a 100W HF transceiver, typically 18A to 22A at 13.8V).
Electrical Resistance ( R R R )
Resistance ( R R R ) is the opposition a material offers to the flow of electric current. As electrons travel through a conductor, they collide with lattice ions, converting electrical energy into heat. The SI unit of resistance is the Ohm ( Ω \Omega Ω ) , named after Georg Simon Ohm.
Materials are categorised by their volumetric resistivity ( ρ \rho ρ ):
Conductors (e.g., copper, silver): Very low resistivity ( ≈ 1.7 × 10 − 8 Ω ⋅ m \approx 1.7 \times 10^{-8}\ \Omega\cdot\text{m} ≈ 1.7 × 1 0 − 8 Ω ⋅ m ), allowing free electron drift.
Insulators (e.g., PTFE/Teflon, ceramic, glass, PVC): Extremely high resistivity ( > 10 12 Ω ⋅ m > 10^{12}\ \Omega\cdot\text{m} > 1 0 12 Ω ⋅ m ), preventing charge movement under normal operating voltages.
Semiconductors (e.g., silicon, germanium): Intermediate resistivity, which can be precisely controlled by introducing impurity atoms (doping).
2. Ohm's Law
Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the potential difference across the two points and inversely proportional to the resistance between them, provided temperature remains constant. Ohm’s Law Formulas: V = I × R ∣ I = V R ∣ R = V I \text{Ohm's Law Formulas: } \quad V = I \times R \quad \vert \quad I = \frac{V}{R} \quad \vert \quad R = \frac{V}{I} Ohm’s Law Formulas: V = I × R ∣ I = R V ∣ R = I V
Where:
- V V V is potential difference in Volts (V)
- I I I is current in Amperes (A)
- R R R is resistance in Ohms ( Ω \Omega Ω )
- Worked Example 1.1: Standard Transceiver Current Draw
An amateur transceiver operating on the 7 MHz (40m) band draws current from a regulated 13.8 V DC 13.8\text{ V DC} 13.8 V DC power supply. If the internal receiver preamp circuit presents a DC load resistance of 184 Ω 184\ \Omega 184 Ω , calculate the current drawn by the preamp circuit.
Solution: I = V R = 13.8 V 184 Ω = 0.075 A = 75 mA I = \frac{V}{R} = \frac{13.8\text{ V}}{184\ \Omega} = 0.075\text{ A} = 75\text{ mA} I = R V = 184 Ω 13.8 V = 0.075 A = 75 mA
3. Series Resistor Circuits
In a series circuit , components are connected end-to-end, forming a single continuous loop for current flow.
Key Properties of Series Circuits:
Current Conservation : The current ( I I I ) flowing through every series element is identical: I total = I 1 = I 2 = ⋯ = I n I_{\text{total}} = I_1 = I_2 = \dots = I_n I total = I 1 = I 2 = ⋯ = I n .
Equivalent Resistance : Total resistance is the sum of all individual resistances: R total = R 1 + R 2 + R 3 + ⋯ + R n R_{\text{total}} = R_1 + R_2 + R_3 + \dots + R_n R total = R 1 + R 2 + R 3 + ⋯ + R n
Voltage Drops : The total applied voltage equals the sum of individual voltage drops across each resistor: V supply = V 1 + V 2 + ⋯ + V n V_{\text{supply}} = V_1 + V_2 + \dots + V_n V supply = V 1 + V 2 + ⋯ + V n .
Property Series Configuration Parallel Configuration
Current Same through all components ( I total = I 1 = I 2 I_{\text{total}} = I_1 = I_2 I total = I 1 = I 2 ) Sum of branch currents ( I total = I 1 + I 2 I_{\text{total}} = I_1 + I_2 I total = I 1 + I 2 )
Voltage Divided across components ( V total = V 1 + V 2 V_{\text{total}} = V_1 + V_2 V total = V 1 + V 2 ) Same across all branches ( V total = V 1 = V 2 V_{\text{total}} = V_1 = V_2 V total = V 1 = V 2 )
Equivalent Resistance R eq = R 1 + R 2 + ⋯ + R n R_{\text{eq}} = R_1 + R_2 + \dots + R_n R eq = R 1 + R 2 + ⋯ + R n 1 R eq = 1 R 1 + 1 R 2 + ⋯ + 1 R n \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n} R eq 1 = R 1 1 + R 2 1 + ⋯ + R n 1
- Failure Effect Open circuit stops all current flow Open branch affects only that specific branch
- 4. Parallel Resistor Circuits
In a parallel circuit , components are connected across the same two common nodes, creating multiple independent current branches.
Key Properties of Parallel Circuits:
Voltage Equality : The potential difference across every parallel branch is identical: V supply = V 1 = V 2 = ⋯ = V n V_{\text{supply}} = V_1 = V_2 = \dots = V_n V supply = V 1 = V 2 = ⋯ = V n .
Current Division : Total supply current equals the sum of currents through each branch: I total = I 1 + I 2 + ⋯ + I n I_{\text{total}} = I_1 + I_2 + \dots + I_n I total = I 1 + I 2 + ⋯ + I n .
Equivalent Resistance : The reciprocal of equivalent resistance is the sum of reciprocals of branch resistances: 1 R total = 1 R 1 + 1 R 2 + ⋯ + 1 R n ⟹ R total = 1 ∑ i = 1 n 1 R i \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n} \implies R_{\text{total}} = \frac{1}{\sum_{i=1}^n \frac{1}{R_i}} R total 1 = R 1 1 + R 2 1 + ⋯ + R n 1 ⟹ R total = ∑ i = 1 n R i 1 1
For two parallel resistors , the simplified "product over sum" formula is: R total = R 1 × R 2 R 1 + R 2 R_{\text{total}} = \frac{R_1 \times R_2}{R_1 + R_2} R total = R 1 + R 2 R 1 × R 2
Note for ACMA Exam : Equivalent resistance of a parallel network is always strictly less than the resistance of the smallest individual resistor in that network.
Worked Example 1.2: Parallel Combination Calculation
Three resistors with values R 1 = 100 Ω R_1 = 100\ \Omega R 1 = 100 Ω , R 2 = 200 Ω R_2 = 200\ \Omega R 2 = 200 Ω , and R 3 = 300 Ω R_3 = 300\ \Omega R 3 = 300 Ω are connected in parallel across a 12 V DC 12\text{ V DC} 12 V DC power source. Calculate:
Total equivalent resistance R total R_{\text{total}} R total .
Total current drawn from the supply I total I_{\text{total}} I total .
Solution: 1 R total = 1 100 + 1 200 + 1 300 = 0.01 + 0.005 + 0.003333 = 0.018333 Ω − 1 \frac{1}{R_{\text{total}}} = \frac{1}{100} + \frac{1}{200} + \frac{1}{300} = 0.01 + 0.005 + 0.003333 = 0.018333\ \Omega^{-1} R total 1 = 100 1 + 200 1 + 300 1 = 0.01 + 0.005 + 0.003333 = 0.018333 Ω − 1 R total = 1 0.018333 ≈ 54.55 Ω R_{\text{total}} = \frac{1}{0.018333} \approx 54.55\ \Omega R total = 0.018333 1 ≈ 54.55 Ω I total = V R total = 12 V 54.55 Ω ≈ 0.220 A = 220 mA I_{\text{total}} = \frac{V}{R_{\text{total}}} = \frac{12\text{ V}}{54.55\ \Omega} \approx 0.220\text{ A} = 220\text{ mA} I total = R total V = 54.55 Ω 12 V ≈ 0.220 A = 220 mA
- 5. Voltage Dividers & Kirchhoff's Circuit Laws
- Unloaded Voltage Divider Rule
A series combination of two resistors acts as a Voltage Divider , scaling down an input voltage to a lower reference value: V out = V in × ( R 2 R 1 + R 2 ) V_{\text{out}} = V_{\text{in}} \times \left( \frac{R_2}{R_1 + R_2} \right) V out = V in × ( R 1 + R 2 R 2 )
Where V out V_{\text{out}} V out is taken across R 2 R_2 R 2 .
Kirchhoff's Current Law (KCL)
Kirchhoff's First Law states that the algebraic sum of currents entering any circuit node (junction) is zero: ∑ I in = ∑ I out \sum I_{\text{in}} = \sum I_{\text{out}} ∑ I in = ∑ I out
KCL reflects the fundamental physical principle of conservation of electrical charge .
Kirchhoff's Voltage Law (KVL)
Kirchhoff's Second Law states that the algebraic sum of all potential differences (voltage sources and voltage drops) around any closed loop is zero: ∑ V = 0 \sum V = 0 ∑ V = 0
KVL reflects the principle of conservation of energy .