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Circuit and electromagnetism basics

How much energy is stored in a 10 µF capacitor charged to 10 V?

  1. A0.5 mJ
  2. B1 mJ
  3. C50 µJ
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Answer: A. 0.5 mJ

The energy in a capacitor is W = (1/2)CV²: (1/2) × 10×10⁻⁶ F × (10 V)² = 5×10⁻⁴ J = 0.5 mJ. The stored charge is Q = CV = 100 µC. Energy is proportional to the square of the voltage, so doubling the voltage quadruples it. Because the energy remains after the supply is switched off, high-voltage capacitors are discharged before being touched.

  • A. Correct. (1/2) × 10 µF × (10 V)² = 0.5 mJ.
  • B. 1 mJ forgets the factor of 1/2.
  • C. 50 µJ forgets to square the voltage.
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