A capacitor of 10 µF is charged to a voltage of 5 V. What is the energy stored i

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Question: A capacitor of 10 µF is charged to a voltage of 5 V. What is the energy stored in the capacitor?

Options:

Correct Answer: 0.25 mJ

Solution:

Energy stored, U = 0.5 * C * V² = 0.5 * 10 x 10^-6 F * (5 V)² = 0.125 mJ.

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

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

Step 1: Identify the values given in the problem. We have a capacitor with a capacitance (C) of 10 microfarads (µF) and a voltage (V) of 5 volts (V).
Step 2: Convert the capacitance from microfarads to farads. 10 µF is equal to 10 x 10^-6 F.
Step 3: Write down the formula for the energy (U) stored in a capacitor: U = 0.5 * C * V².
Step 4: Substitute the values into the formula. U = 0.5 * (10 x 10^-6 F) * (5 V)².
Step 5: Calculate (5 V)², which is 25 V².
Step 6: Now substitute this value back into the equation: U = 0.5 * (10 x 10^-6 F) * 25 V².
Step 7: Multiply 0.5 by 10 x 10^-6 F to get 5 x 10^-6 F.
Step 8: Now multiply 5 x 10^-6 F by 25 to get 125 x 10^-6 J.
Step 9: Convert 125 x 10^-6 J to millijoules (mJ). Since 1 J = 1000 mJ, we have 0.125 mJ.

Capacitance and Energy Storage – The relationship between capacitance, voltage, and energy stored in a capacitor, given by the formula U = 0.5 * C * V².