NEIEP Mechanics Practice Exam

What happens to the power consumed if you double the voltage across a resistor while keeping the resistance constant?

1. The power remains the same

2. The power is halved

3. The power is doubled

4. The power is quadrupled

The correct answer is: The power is doubled

When the voltage across a resistor is doubled while keeping the resistance constant, the power consumed by the resistor increases significantly. This relationship is described by Ohm's Law and the power formula. According to Ohm's law, the current (I) through a resistor can be calculated using the formula \( I = \frac{V}{R} \), where V is the voltage, and R is the resistance. The power (P) consumed in an electrical circuit can be represented by the formula \( P = V \times I \). Substituting Ohm's Law into the power formula gives \( P = V \times \frac{V}{R} \) or \( P = \frac{V^2}{R} \). When you double the voltage (let’s say the original voltage is V, and you increase it to 2V), the new power consumption can be calculated as follows: - Original power: \( P_1 = \frac{V^2}{R} \) - New power after doubling voltage: \( P_2 = \frac{(2V)^2}{R} = \frac{4V^2}{R} \) Comparing the new power and the original power shows that