The power dissipated by a resistor, in watts, is equal to the square of the current, in amperes, multiplied by...
GMAT Advanced Math : (Adv_Math) Questions
The power dissipated by a resistor, in watts, is equal to the square of the current, in amperes, multiplied by the resistance, in ohms. What is the current, in amperes, flowing through a \(\mathrm{2}\)-ohm resistor that dissipates \(\mathrm{32}\) watts of power?
- 2
- 4
- 6
- 16
2
4
6
16
1. TRANSLATE the problem information
- Given information:
- Power dissipated: 32 watts
- Resistance: 2 ohms
- Power formula: \(\mathrm{Power} = (\mathrm{current})^2 \times \mathrm{resistance}\)
- TRANSLATE this formula: \(\mathrm{P} = \mathrm{I}^2\mathrm{R}\)
2. INFER the solution strategy
- We have P and R, need to find I
- Substitute known values into \(\mathrm{P} = \mathrm{I}^2\mathrm{R}\) and solve for I
3. SIMPLIFY by substituting and solving
- Substitute the values: \(32 = \mathrm{I}^2(2)\)
- Simplify: \(32 = 2\mathrm{I}^2\)
- Divide both sides by 2: \(\mathrm{I}^2 = 16\)
- Take the square root: \(\mathrm{I} = \pm 4\)
- Since current is positive in this context: \(\mathrm{I} = 4\) amperes
Answer: B (4)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students may confuse the relationship between variables in the power formula. Some might think \(\mathrm{P} = \mathrm{IR}\) (confusing with Ohm's law) rather than \(\mathrm{P} = \mathrm{I}^2\mathrm{R}\), or mix up which variable they're solving for.
This confusion leads them to set up incorrect equations and arrive at wrong answers, potentially selecting Choice A (2) or Choice D (16).
Second Most Common Error:
Poor SIMPLIFY execution: Students correctly set up \(32 = 2\mathrm{I}^2\) but make arithmetic errors. They might divide incorrectly (getting \(\mathrm{I}^2 = 64\) instead of \(\mathrm{I}^2 = 16\)) or make errors when taking the square root.
Arithmetic mistakes during simplification could lead them to select Choice D (16) if they confuse \(\mathrm{I}^2 = 16\) with \(\mathrm{I} = 16\), or other incorrect choices.
The Bottom Line:
This problem tests whether students can translate a physics relationship into mathematical form and then execute basic algebraic solving. The key challenge is recognizing that power involves current squared, not just current, which distinguishes this from simpler electrical formulas.
2
4
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16