Fundamentals of Series DC Electrical Circuits

Fundamentals of Direct Current (DC)

• Current in DC flows in a single direction with relatively steady voltage.

• The waveform is an analog signal where ramping up or down is caused by changing magnetic fields within the circuit.

Series DC Circuit Characteristics

• Configuration: All electrical components are connected in a single line (one loop).

• Current ($I$): The current value remains constant throughout the entire circuit ($I_T = I_1 = I_2 = I_3 = \dots$).

• Continuity: A continuous path is required for current flow; an open circuit stops all flow.

• Nodes: Points where current splits into various paths (applicable to complex/parallel circuits, whereas series follows one path).

Resistance in Series ($R_T$)

• The total resistance is the sum of all individual resistances: $R_T = R_1 + R_2 + R_3 + \dots$

• Landing Light Scenario: Three bulbs with resistances of $2\,\Omega$, $3\,\Omega$, and $5\,\Omega$ result in $R_T = 10\,\Omega$.

• Windshield Wiper Motor: Two parts with $4\,\Omega$ and $6\,\Omega$ result in $R_T = 10\,\Omega$.

• Runway Lighting: Six lamps in series, each at $8\,\Omega$, result in $R_T = 48\,\Omega$.

Voltage Drops and Kirchhoff’s Voltage Law (KVL)

• Terminology: Voltage drop is the reduction in electrical potential as current flows through a conductor or component.

• Energy Conversion: Loads convert electrical potential into heat, light, motion, or sound.

• Source Equality: In a series circuit, $E_T = E_1 + E_2 + E_3 + \dots$

• Kirchhoff’s Voltage Law: The sum of all voltages around any closed loop must equal zero ("What goes in must be used").

Power Consumption ($P$)

• Power is measured in Watts ($W$).

• Calculation: $P = E \times I$.

• Total Power: For DC, total circuit power is additive across all loads.

Calculation Examples

• Example 1 (Twin-engine Aircraft): Given $E_T = 18\,V$, $I_T = 3\,A$, $R_1 = 2\,\Omega$, $R_2 = 3\,\Omega$, and $E_3 = 3\,V$.

  • Calculated: $E_1 = 6\,V$, $E_2 = 9\,V$, $R_3 = 1\,\Omega$, $R_T = 6\,\Omega$, and $P_T = 54\,W$.

• Example 2 (Turboprop Starter-Generator): Given $E_T = 120\,V$, $I_T = 5\,A$, and $R_1 = 4\,\Omega$.

  • Calculated: $E_1 = 20\,V$, $E_2 = 100\,V$, $R_2 = 20\,\Omega$, $R_T = 24\,\Omega$, and $P_T = 600\,W$.

• Example 3 (Corporate Jet Landing Light): Given $E_T = 150\,V$, $I_T = 10\,A$, and $E_1 = 50\,V$.

  • Calculated: $E_2 = 100\,V$, $R_T = 15\,\Omega$, $R_1 = 5\,\Omega$, $R_2 = 10\,\Omega$, and $P_T = 1500\,W$.

Voltage Sources in Series

• Power sources can be combined by connecting the positive terminal of one to the negative terminal of the next.

• Combining sources in this manner provides higher total voltage.

Questions & Discussion

• Q: Is the DC waveform a signal?

• A: Yes, it is an analog signal. The ramp up/down is caused by the increasing/decreasing magnetic field in the circuit.

• Debrief Focus: The session concluded with a review of series circuit laws, Ohm's law applications, and the physical reasons for voltage drops as potential energy converts to other forms.