Question

Difficulty: MediumSeries Circuits

In direct current (DC) electronics, circuit modifications and faults alter overall circuit parameters. Match each series circuit condition on the left with its correct electrical effect on the right.

  • Adding an additional resistor in series with existing loadsTotal circuit resistance increases, which causes total loop current to decrease.
  • Developing a complete open circuit at one componentThe single conductive loop is broken, reducing total circuit current to zero amperes.
  • Placing a direct short circuit across one of several series resistorsTotal equivalent resistance decreases, causing loop current and remaining voltage drops to increase.
  • Doubling the applied source voltage across the unchanged series stringTotal circuit current and all individual resistor voltage drops double proportionally.

Answer

Adding a series resistor increases total resistance and decreases loop current; an open circuit drops current to zero; shorting a resistor reduces total resistance and increases current and remaining voltage drops; doubling source voltage doubles both total current and individual voltage drops.
In a series circuit, current flows through a single continuous path. Total resistance is the sum of all individual resistances (RT=R1+R2+…R_T = R_1 + R_2 + \dots). Adding a resistor increases total resistance, reducing current. Shorting a resistor bypasses that element, lowering total resistance and increasing loop current, which increases the voltage drop across the remaining resistors (V=I×RV = I \times R). An open circuit breaks the loop, reducing current to zero. Doubling the source voltage across a fixed total resistance doubles the current and doubles each individual voltage drop proportionally.

Step-by-Step Solution

1
Analyze the resistance relationship for series circuits.
Total resistance is the direct sum of all individual resistors: RT=R1+R2+⋯+RnR_T = R_1 + R_2 + \dots + R_n.
Adding a resistor increases RTR_T, while shorting out a resistor removes its resistance from the sum, lowering RTR_T.
2
Apply Ohm's Law (I=VTRTI = \frac{V_T}{R_T}) to determine current behavior under each modification.
Higher resistance reduces current, lower resistance increases current, and doubled voltage with fixed resistance doubles current.
Current is directly proportional to voltage and inversely proportional to total circuit resistance.
3
Evaluate the single-path property of a series circuit under open fault conditions.
An open circuit provides infinite resistance (R=∞R = \infty), causing I=0 AI = 0\text{ A}.
A continuous closed path is mandatory for current flow in any series circuit.

Key Concept

Series Circuit Governing Rules and Fault Characteristics
Estimated Time:1m 15s
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