To find the energy stored in a capacitor, we can use the formula: \[ U = \frac{1}{2} C V^2 \] where: - \( U \) is the energy stored in the capacitor (in joules), - \( C \) is the capacitance (in farads), - \( V \) is the voltage across the capacitor (in volts). However, we are given the charge \( Q \) instead of the voltage. We can relate charge and voltage using the formula: \[ Q = C V \] From this, we can express voltage \( V \) as: \[ V = \frac{Q}{C} \] Now, substituting this expression for \( V \) back into the energy formula gives us: \[ U = \frac{1}{2} C \left(\frac{Q}{C}\right)^2 \] This simplifies to: \[ U = \frac{1}{2} \frac{Q^2}{C} \] ### Step-by-Step Calculation 1. **Identify the values**: - Capacitance \( C = 10 \, \mu F = 10 \times 10^{-6} \, F = 10^{-5} \, F \) - Charge \( Q = 100 \, \mu C = 100 \times 10^{-6} \, C = 10^{-4} \, C \) 2. **Substitute the values into the energy formula**: \[ U = \frac{1}{2} \frac{(10^{-4})^2}{10 \times 10^{-6}} \] 3. **Calculate \( (10^{-4})^2 \)**: \[ (10^{-4})^2 = 10^{-8} \] 4. **Substitute this back into the equation**: \[ U = \frac{1}{2} \frac{10^{-8}}{10 \times 10^{-6}} = \frac{1}{2} \frac{10^{-8}}{10^{-5}} = \frac{1}{2} \times 10^{-3} \] 5. **Calculate the final value**: \[ U = \frac{1}{2} \times 10^{-3} = 0.5 \times 10^{-3} = 5 \times 10^{-4} \, J \] ### Conclusion The energy stored in the capacitor is: \[ U = 5 \times 10^{-4} \, J \] Thus, the correct option is **D. 5 x 10^-4 J**. ### Explanation of Other Options - **Option A: 5 x 10^4 J**: This value is far too large for the given capacitance and charge. The energy stored in capacitors is typically in the range of microjoules to millijoules for small capacitances and charges. - **Option B: 4 x 10^2 J**: Similar to option A, this value is also excessively high for the parameters given. It does not align with the expected energy levels for a capacitor of 10μF and 100μC. - **Option C: 4 x 10^-3 J**: This value is larger than our calculated energy of 5 x 10^-4 J. It suggests a misunderstanding of the relationship between charge, capacitance, and energy. ### Revision Summary - The energy stored in a capacitor can be calculated using \( U = \frac{1}{2} \frac{Q^2}{C} \). - Always convert units to standard SI units (farads for capacitance, coulombs for charge). - Ensure calculations are done step-by-step to avoid errors. - The correct answer for the energy stored in a 10μF capacitor with a charge of 100μC is **5 x 10^-4 J**.