Effect of removing a series element: When one of three series resistors is removed and the circuit is reconnected across the same source, how does the current change?

Difficulty: Easy

Correct Answer: increases

Explanation:


Introduction / Context:
Current in a circuit depends on total resistance for a fixed source voltage. Removing a series element reduces total resistance, which in turn increases current according to Ohm's law. This qualitative question probes your grasp of that inverse relationship without requiring specific numbers.


Given Data / Assumptions:

  • Original circuit: three resistors in series.
  • Modified circuit: one of the three series resistors is removed; the remaining two are still in series with the same source.
  • Source voltage remains unchanged; ideal conditions.


Concept / Approach:
Total resistance for three in series is R_total(3) = R1 + R2 + R3. After removing one, R_total(2) = R1 + R2 (or similar). Since R_total(2) < R_total(3), Ohm’s law dictates I_new = V / R_total(2) > V / R_total(3) = I_old. The exact percentage change depends on the actual values, not necessarily “one-third.”


Step-by-Step Solution:

Recognize that series removal lowers total resistance.With fixed V, current varies inversely with total resistance.Thus, the loop current must increase after removing one resistor.


Verification / Alternative check:
Numeric example: Let R1 = R2 = R3 = 100 Ω. Initially R_total = 300 Ω, I_old = V/300. After removing one, R_total = 200 Ω, I_new = V/200 = 1.5 * I_old. That is an increase, not necessarily “by one-third.”


Why Other Options Are Wrong:

  • Increases by one-third: The change depends on actual values; equal resistors give a 50% increase, not 33%.
  • Decreases by one-third: Removing a series resistor cannot decrease current for a fixed source.
  • Decreases by the amount of current through the removed resistor: Nonsense in a series path; current is the same through all elements and does not “subtract.”


Common Pitfalls:

  • Assuming a fixed percentage change without numeric context.
  • Confusing current division (a parallel concept) with series behavior.


Final Answer:
increases

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