If the charge stored on a capacitor is quadrupled while the capacitance remains unchanged, by what factor does the energy stored increase?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $25.99Unlock all

Study for the UCF PHY2054 General Physics Exam. Use flashcards and multiple-choice questions complete with hints and explanations. Boost your understanding and get exam-ready!

Multiple Choice

If the charge stored on a capacitor is quadrupled while the capacitance remains unchanged, by what factor does the energy stored increase?

Explanation:
Energy stored in a capacitor scales with the square of the charge when the capacitance is fixed, since U = Q^2/(2C) (or equivalently U = (1/2) C V^2 with V = Q/C). If the charge is quadrupled, Q → 4Q, then U → (4Q)^2/(2C) = 16 Q^2/(2C) = 16 U. Equivalently, the voltage becomes four times larger (V → 4V), and U → (1/2) C (4V)^2 = 16 U. So the energy increases by a factor of 16.

Energy stored in a capacitor scales with the square of the charge when the capacitance is fixed, since U = Q^2/(2C) (or equivalently U = (1/2) C V^2 with V = Q/C). If the charge is quadrupled, Q → 4Q, then U → (4Q)^2/(2C) = 16 Q^2/(2C) = 16 U. Equivalently, the voltage becomes four times larger (V → 4V), and U → (1/2) C (4V)^2 = 16 U. So the energy increases by a factor of 16.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy