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Calculate the energy stored in a capacitor with capacitance 8 ext esizebox0.5em! extµF and voltage 10 ext V.

Physics

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Step-by-step solution

4 steps

  1. Identify the given values from the diagram.

    The capacitance of the capacitor is C=8μFC = 8 \mu F.
    The voltage across the capacitor is V=10VV = 10 V.

  2. Convert the capacitance to Farads.

    C=8μF=8×10−6FC = 8 \mu F = 8 \times 10^{-6} F

  3. Use the formula for the energy stored in a capacitor.

    The energy EE stored in a capacitor is given by the formula:

    E=12CV2E = \frac{1}{2}CV^2

  4. Substitute the values into the formula and calculate the energy.

    E=12(8×10−6F)(10V)2E = \frac{1}{2} (8 \times 10^{-6} F) (10 V)^2 E=12(8×10−6F)(100V2)E = \frac{1}{2} (8 \times 10^{-6} F) (100 V^2) E=(4×10−6)×100JE = (4 \times 10^{-6}) \times 100 J E=400×10−6JE = 400 \times 10^{-6} J E=4×10−4JE = 4 \times 10^{-4} J

    The energy stored in the capacitor is \boxed{\text{4 \times 10^{-4} J}}.

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