Ohm’s law application (conceptual): If the voltage across a fixed resistance doubles (R is constant and linear), what happens to the current through that resistance?

Introduction:
Ohm’s law is a fundamental relationship for linear resistive elements. It directly ties voltage (V), current (I), and resistance (R) through the simple formula V = I * R. Interpreting qualitative changes—like “what if we double the voltage?”—is a core skill in basic circuit analysis and troubleshooting.

Given Data / Assumptions:

• The element is a fixed, linear resistor (R is constant).
• The voltage across the resistor is doubled.
• Temperature and nonlinearity effects are ignored.

Concept / Approach:

From V = I * R, for a constant R, current is proportional to voltage: I = V / R. If V is scaled by a factor k, current scales by the same factor k. Therefore, when the voltage doubles (k = 2), the current must also double, provided R does not change and the device remains in its linear region.

Step-by-Step Solution:

Verification / Alternative check:

Pick numbers to validate: let R = 10 Ω, V1 = 5 V → I1 = 0.5 A. Double voltage to V2 = 10 V → I2 = 1.0 A, which is exactly double. This numerical trial confirms the proportionality.

Why Other Options Are Wrong:

• the current is halved: Would require voltage to halve or resistance to double, neither stated.
• the resistance doubles: R is fixed by the problem statement.
• the current is unchanged: Only true if voltage is unchanged or R → ∞.

Common Pitfalls:

• Confusing changes in V with changes in R; in this scenario R is constant.
• Applying Ohm’s law to non-ohmic devices (e.g., lamps, diodes) where I–V is nonlinear.

Final Answer:

none of the above