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Difficulty: MediumSeries Circuits

In direct-current (DC) series circuit analysis, distinct electrical principles govern how current, voltage, resistance, and faults behave across a single closed pathway. Match each series circuit parameter or condition on the left with its correct governing rule on the right.

  • Total equivalent resistance (RTR_T)Equals the direct sum of all individual resistive values (R1+R2+R3+…R_1 + R_2 + R_3 + \dots)
  • Circuit current (II)Remains constant in magnitude at every point throughout the single conductive path
  • Total source voltage (VTV_T)Equals the sum of the individual voltage drops across all connected loads (V1+V2+V3+…V_1 + V_2 + V_3 + \dots)
  • Open-circuit fault in any single componentImmediately halts all current flow and drops circuit current to zero amperes

Answer

Total equivalent resistance matches the direct sum of all individual resistive values; Circuit current matches remaining constant at every point; Total source voltage matches the sum of the individual voltage drops across all loads; An open-circuit fault matches immediately halting all current flow.
Series circuits are defined by a single pathway for current. Consequently, current (II) is identical at all points, total resistance (RTR_T) is the arithmetic sum of the component resistances, total voltage (VTV_T) equals the sum of the individual component voltage drops, and an interruption anywhere breaks the complete circuit, dropping total current to zero.

Step-by-Step Solution

1
Identify the resistance relationship for series circuits.
Total resistance increases with each added resistor and is found by adding resistances directly (RT=R1+R2+…R_T = R_1 + R_2 + \dots).
Electrons must pass sequentially through every resistive element along the single pathway.
2
Determine the current distribution rule in a single-loop circuit.
Current magnitude is uniform everywhere (IT=I1=I2I_T = I_1 = I_2).
Charge cannot accumulate or branch off in an unbranched series loop.
3
Apply Kirchhoff's Voltage Law to the series loop.
Total applied voltage equals the sum of the series voltage drops (VT=V1+V2+…V_T = V_1 + V_2 + \dots).
The electrical potential energy supplied by the source must be completely dissipated across the series loads.
4
Evaluate the effect of an open-circuit fault.
An open condition creates infinite resistance, stopping all loop current (I=0 AI = 0\text{ A}).
A continuous physical path is required for DC electron flow.

Key Concept

Fundamental series circuit characteristics: additive resistance, constant current, additive voltage drops (Kirchhoff's Voltage Law), and single-point failure dependency.
Estimated Time:1m 0s
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Topics

Series Circuits

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