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A capacitor of capacitance 100 μF is charged to a potential difference of 20 V - Leaving Cert Physics - Question e - 2005

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A capacitor of capacitance 100 μF is charged to a potential difference of 20 V. What is the energy stored in the capacitor?

Worked Solution & Example Answer:A capacitor of capacitance 100 μF is charged to a potential difference of 20 V - Leaving Cert Physics - Question e - 2005

Step 1

Energy Stored in the Capacitor Formula

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Answer

The energy stored in a capacitor can be calculated using the formula:
E=12CV2E = \frac{1}{2} C V^2
where:

  • EE is the energy stored in joules (J),
  • CC is the capacitance in farads (F), and
  • VV is the potential difference in volts (V).

Step 2

Substituting Values

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Answer

Now, substituting the given values into the formula:

  • Capacitance C=100μF=100×10−6FC = 100 \mu F = 100 \times 10^{-6} F
  • Potential difference V=20VV = 20 V.
    Thus,
    E=12×(100×10−6)×(20)2E = \frac{1}{2} \times (100 \times 10^{-6}) \times (20)^2.

Step 3

Calculating Energy

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Answer

Calculating the expression:

  1. First calculate 202=40020^2 = 400.
  2. Then multiply by the capacitance:
    E=12×(100×10−6)×400E = \frac{1}{2} \times (100 \times 10^{-6}) \times 400
  3. This simplifies to:
    E=0.02JE = 0.02 J.

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