Ohm’s law in a series circuit: If the total resistance in a series circuit doubles while the applied source voltage remains constant, how will the circuit current change?

Introduction / Context:
This question tests core understanding of Ohm’s law and how current behaves in a simple series circuit when total resistance changes. In many troubleshooting and design scenarios, recognizing proportional relationships between current, resistance, and voltage is essential for quick, reliable reasoning.

Given Data / Assumptions:

• Total resistance in a series circuit doubles.
• The source (supply) voltage is constant.
• Ideal components with no temperature-induced resistance change during comparison.
• Single-loop series circuit so one current flows through all elements.

Concept / Approach:
Ohm’s law states I = V / R. If V is constant and R increases, I must decrease proportionally. Specifically, if R becomes 2R, then I becomes V / (2R) = (1/2) * (V / R). Thus current is halved. This inverse proportionality between current and resistance at fixed voltage is a cornerstone of basic circuit analysis.

Step-by-Step Solution:
Initial current: I1 = V / R_total.After doubling resistance: R_new = 2 * R_total.New current: I2 = V / R_new = V / (2 * R_total) = (1/2) * (V / R_total).Therefore, I2 = I1 / 2, i.e., the current is halved.

Verification / Alternative check:
Use numerical example. Let V = 10 V and R_total = 100 Ω → I1 = 10 / 100 = 0.1 A. If resistance doubles to 200 Ω → I2 = 10 / 200 = 0.05 A, exactly half. The numerical check confirms the proportional reasoning.

Why Other Options Are Wrong:
Be the same: would require resistance unchanged or voltage doubled to compensate; not our case.Be doubled: happens if resistance halves at constant voltage, not when it doubles.Reduce source voltage: the source voltage is given as constant; the current change does not “reduce” the source.

Common Pitfalls:
Confusing proportional and inverse proportional relationships. Remember: at constant V, current varies inversely with resistance (I ∝ 1/R). At constant R, current varies directly with voltage (I ∝ V).

Final Answer:
be halved