A capacitor of capacitance 5μF is charged to a potential of 10V. What is the energy stored in the capacitor?

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Q: A capacitor of capacitance 5μF is charged to a potential of 10V. What is the energy stored in the capacitor?

Solution: Energy stored U = 1/2 * C * V² = 1/2 * 5 × 10^-6 F * (10 V)² = 0.5 mJ.

Steps: 9

Step 1: Identify the values given in the problem. The capacitance (C) is 5 microfarads (μF) and the voltage (V) is 10 volts (V).
Step 2: Convert the capacitance from microfarads to farads. 5 μF = 5 × 10^-6 F.
Step 3: Write down the formula for the energy (U) stored in a capacitor: U = 1/2 * C * V².
Step 4: Substitute the values into the formula. U = 1/2 * (5 × 10^-6 F) * (10 V)².
Step 5: Calculate (10 V)², which is 100 V².
Step 6: Now substitute this value back into the equation: U = 1/2 * (5 × 10^-6 F) * 100 V².
Step 7: Multiply 5 × 10^-6 F by 100 to get 5 × 10^-4 F·V².
Step 8: Now calculate U = 1/2 * (5 × 10^-4) = 2.5 × 10^-4 joules.
Step 9: Convert joules to millijoules. 2.5 × 10^-4 joules = 0.25 mJ.