3.1 Ohm's Law, Series, and Parallel Circuits

Why This Matters in Aviation Maintenance

For an aircraft maintenance engineer (AME) holding an EASA Part-66 license, the ability to analyze and troubleshoot Direct Current (DC) circuits is fundamental. Aircraft systems—ranging from primary power distribution to avionics, cockpit lighting, and landing gear controls—depend heavily on DC power. When a landing light fails to illuminate or a circuit breaker trips, you must be able to use basic circuit laws to isolate the fault. Is it a short circuit (zero resistance, high current), an open circuit (infinite resistance, zero current), or a high-resistance contact due to corrosion? Applying Ohm’s Law and understanding series-parallel configurations is the first line of defense in keeping an aircraft airworthy.

Conventional Flow vs. Electron Flow

Before performing calculations, it is critical to distinguish between the two conventions used to describe electrical current:

1. Conventional Flow: Proposed by Benjamin Franklin, this convention assumes that electrical current is the flow of positive charge carriers from the positive (+) terminal of a voltage source, through the external circuit, and back to the negative (-) terminal. Almost all engineering block diagrams, schematic symbols (such as diode arrows), and standard electrical rules (like Fleming's Left- and Right-Hand Rules) are based on conventional flow.
2. Electron Flow: With the discovery of the electron, physicists established that current in solid conductors is actually the movement of negatively charged electrons. Since like charges repel and opposites attract, electrons flow from the negative (-) terminal (where they are in excess) to the positive (+) terminal (where there is a deficit).

For numerical calculations of current magnitude, resistance, and power, both models yield identical results. However, when analyzing semiconductor devices or reading specialized aircraft schematics, you must verify which convention is active to avoid polarity errors.

Ohm's Law (V = I * R)

Ohm's Law states that the current (I) flowing through a metallic conductor at a constant temperature is directly proportional to the potential difference (V) across it and inversely proportional to its resistance (R).

Mathematically, this is expressed as:

V = I * R

Where:

• Voltage (V): Electromotive force or potential difference, measured in Volts (V).
• Current (I): The rate of flow of electric charge, measured in Amperes (A).
• Resistance (R): The opposition to the flow of current, measured in Ohms (Ω).

From this primary equation, we derive:

• I = V / R (Current increases if voltage increases or resistance decreases)
• R = V / I (Resistance of a component is the ratio of the voltage across it to the current through it)

Electrical Power and Heat Dissipation

Electrical power (P) is the rate at which electrical energy is converted into another form of energy (typically heat in a resistor). It is measured in Watts (W).

The primary power equation is:

P = V * I

By substituting Ohm's Law (V = I * R and I = V / R), we obtain two other extremely useful formulas:

• P = I^2 * R (Power is proportional to the square of the current)
• P = V^2 / R (Power is inversely proportional to the resistance for a constant voltage)

Resistors are rated not only by their resistance value in Ohms but also by their power handling capability in Watts (e.g., 0.25W, 1W, 10W). If a resistor in an aircraft instrument panel is replaced with one of a lower power rating, even if the resistance is identical, it will overheat, fail, and potentially cause a fire. When current through a circuit doubles, the power dissipated as heat quadruples (I^2), which is why current overloads are so hazardous.

Series DC Circuits

A series circuit is a circuit in which components are connected end-to-end, providing only a single path for current to flow.

Characteristics of Series Circuits:

1. Constant Current: The current is the same through every component in the circuit. I_total = I_1 = I_2 = I_3 = ...
2. Additive Resistance: The total equivalent resistance (R_total) is the sum of the individual resistances. R_total = R_1 + R_2 + R_3 + ...
3. Additive Voltage Drops: The total voltage supplied by the source equals the sum of the individual voltage drops across each resistor. V_source = V_1 + V_2 + V_3 + ... Where each drop is calculated as V_n = I * R_n.

Worked Exam Scenario: Series Circuit

An aircraft warning light circuit consists of a 28 V DC power bus, a dimmer resistor of 40 Ohms, and a warning lamp with a hot resistance of 16 Ohms connected in series.

1. Total Resistance (R_total): R_total = R_dimmer + R_lamp = 40 + 16 = 56 Ohms
2. Circuit Current (I): I = V_source / R_total = 28 / 56 = 0.5 A
3. Voltage Drop across the Lamp (V_lamp): V_lamp = I * R_lamp = 0.5 * 16 = 8 V
4. Power Dissipated by the Dimmer Resistor (P_dimmer): P_dimmer = I^2 * R_dimmer = (0.5)^2 * 40 = 0.25 * 40 = 10 W

Parallel DC Circuits

A parallel circuit is a circuit in which components are connected across the same two nodes, creating multiple branches or paths for current to flow.

Characteristics of Parallel Circuits:

1. Constant Voltage: The voltage across each branch of a parallel circuit is identical and equal to the source voltage. V_source = V_1 = V_2 = V_3 = ...
2. Additive Currents: The total current leaving the source is the sum of the currents flowing through each parallel branch. I_total = I_1 + I_2 + I_3 + ...
3. Reciprocal Equivalent Resistance: The reciprocal of the total resistance is equal to the sum of the reciprocals of the individual branch resistances. 1 / R_total = 1 / R_1 + 1 / R_2 + 1 / R_3 + ... For two parallel resistors, this simplifies to the product-over-sum formula: R_total = (R_1 * R_2) / (R_1 + R_2)

The total equivalent resistance of any parallel network is always less than the resistance of the smallest individual branch resistor. This is because adding parallel paths increases the overall conductance (the ease with which current flows).

Worked Exam Scenario: Parallel Circuit

Two auxiliary heating elements are connected in parallel across a 120 V DC bus. Element 1 has a resistance of 20 Ohms, and Element 2 has a resistance of 30 Ohms.

1. Equivalent Resistance (R_total): R_total = (R_1 * R_2) / (R_1 + R_2) = (20 * 30) / (20 + 30) = 600 / 50 = 12 Ohms
2. Total Bus Current (I_total): I_total = V_source / R_total = 120 / 12 = 10 A
3. Individual Branch Currents:
   • I_1 = V_source / R_1 = 120 / 20 = 6 A
   • I_2 = V_source / R_2 = 120 / 30 = 4 A
   • Verify: I_total = I_1 + I_2 = 6 + 4 = 10 A

Summary Table: Series vs. Parallel

Exam Pitfalls and Tips

• The Conductance Trap: When calculating parallel resistance, don't forget to take the final reciprocal. A common error on the EASA exam is calculating 1/R_total = 1/6 + 1/3 = 3/6 = 0.5 and selecting 0.5 Ohms as the answer, forgetting to invert it to find R_total = 2 Ohms.
• The Dimmer Resistor Power Rating: Always verify the power dissipation formula when troubleshooting. Dimmer resistors in older cockpits generate significant heat. A high current draw through a partially dimmed lamp can quickly cook a replacement resistor that has an inadequate power rating.