For a fixed resistance R, if the applied voltage across it is increased by a factor of five (steady DC), by what factor does the current change?

Introduction:
Understanding proportionality in Ohm's law enables quick mental calculations in circuit design and testing. This question tests the ability to scale current when voltage is scaled with resistance held constant.

Given Data / Assumptions:

• Fixed resistance R (constant with voltage and temperature).
• DC operation with a constant-voltage source.
• No additional reactive components.

Concept / Approach:
Ohm's law: I = V / R. With R fixed, current is directly proportional to voltage. Therefore, scaling V by a factor k scales I by the same factor k. Here k = 5, so current increases fivefold.

Step-by-Step Solution:
1) Original current: I1 = V1 / R.2) New voltage: V2 = 5 * V1.3) New current: I2 = V2 / R = (5 * V1) / R = 5 * (V1 / R) = 5 * I1.4) Therefore, current increases by factor 5.

Verification / Alternative check:
Example numbers: R = 10 Ω, V1 = 2 V → I1 = 0.2 A. Increase voltage to 10 V → I2 = 1 A, which is 5 times larger.

Why Other Options Are Wrong:
Decreases fivefold: contradicts direct proportionality.
Stays the same or not enough information: Ohm's law determines the result fully.
Increases by 25: would be true for quantities proportional to V^2 (power), not current.

Common Pitfalls:
Mixing up current with power. Power P = V * I = V^2 / R grows with the square of voltage, but current grows linearly with voltage when R is fixed.

Final Answer:
It increases by a factor of five.