Power dissipation in unequal parallel resistors When three different resistor values are connected in parallel, which branch experiences the greatest power loss (for the same applied voltage)?

Introduction / Context:
Understanding how power distributes among branches in a parallel network is essential for thermal design and component selection. Overheating typically occurs in the branch with the highest dissipation, so predicting which branch that is prevents premature failures.

Given Data / Assumptions:

• Three resistors of unequal value connected in parallel across the same source.
• Ideal conditions: wires and source internal resistance neglected.
• Steady DC operation.

Concept / Approach:
In parallel circuits, the voltage across each resistor is identical. Power in a resistor can be computed as P = V^2/R. With a common V, the branch power is inversely proportional to resistance. Therefore, the smallest resistance draws the largest current and dissipates the most power.

Step-by-Step Solution:

Verification / Alternative check:
Using P = I^2 * R with I = V/R in parallel gives P = (V/R)^2 * R = V^2 / R, the same conclusion: smallest R gives largest power.

Why Other Options Are Wrong:

• Largest resistance: has the lowest current and lowest P = V^2/R.
• Same power loss: only true if all resistances were equal.
• Need more values: not necessary; the relationship holds for any positive unequal resistances.

Common Pitfalls:
Applying the series-circuit intuition where current is common; in parallel, voltage is common, changing the power relationship with resistance.

Final Answer:
The smallest resistance