Which formula explicitly shows a direct proportionality between electrical power and voltage (holding the other variable constant)?

Introduction / Context:
Power relations in circuits are derived from Ohm’s law and definitions of work/energy. Recognizing which expression portrays direct proportionality with voltage is useful when reasoning about how power scales as supply voltage changes.

Given Data / Assumptions:

• Standard definitions: P = V * I, V = I * R.
• We consider proportionality while holding one variable constant.

Concept / Approach:
The definition of electric power in any circuit is P = V * I. If current I is held constant (for example, an ideal current source), then P is directly proportional to V. Alternative forms (P = V^2 / R or P = I^2 * R) change the variable being held constant and do not show simple linear proportionality with V alone unless R or I is constant.

Step-by-Step Solution:
Start from P = V * I.If I is fixed, P ∝ V (a straight-line relationship).Hence, among the options, P = VI directly shows power increasing with voltage when current is constant.

Verification / Alternative check:
Holding R constant gives P = V^2 / R, a quadratic dependence on V, not a direct linear proportionality. Thus P = VI is the cleanest expression of direct proportionality under constant current conditions.

Why Other Options Are Wrong:

• V = IR and I = V/R: These are Ohm’s law relations, not power formulas.
• P = IR: Dimensional mismatch; correct form is P = I^2 * R or P = V^2 / R.

Common Pitfalls:

• Confusing “direct proportionality” (linear) with “depends on.”
• Forgetting to specify which variable is held constant when discussing proportionality.

Final Answer:
P = VI