A capacitor stores 5 microfarads of charge at a voltage of 10 volts. What is the energy stored in the capacitor?
Practice Questions
1 question
Q1
A capacitor stores 5 microfarads of charge at a voltage of 10 volts. What is the energy stored in the capacitor?
0.25 mJ
0.5 mJ
0.75 mJ
1 mJ
The energy stored in a capacitor is given by the formula E = 0.5 * C * V^2. Here, E = 0.5 * 5 * 10^-6 F * (10 V)^2 = 0.5 * 5 * 10^-6 * 100 = 0.25 mJ.
Questions & Step-by-step Solutions
1 item
Q
Q: A capacitor stores 5 microfarads of charge at a voltage of 10 volts. What is the energy stored in the capacitor?
Solution: The energy stored in a capacitor is given by the formula E = 0.5 * C * V^2. Here, E = 0.5 * 5 * 10^-6 F * (10 V)^2 = 0.5 * 5 * 10^-6 * 100 = 0.25 mJ.
Steps: 9
Step 1: Identify the values given in the problem. We have a capacitance (C) of 5 microfarads and a voltage (V) of 10 volts.
Step 2: Convert microfarads to farads. 5 microfarads is equal to 5 * 10^-6 farads.
Step 3: Write down the formula for the energy (E) stored in a capacitor: E = 0.5 * C * V^2.
Step 4: Substitute the values into the formula. E = 0.5 * (5 * 10^-6 F) * (10 V)^2.
Step 5: Calculate (10 V)^2, which is 100 V^2.
Step 6: Now substitute this value back into the equation: E = 0.5 * (5 * 10^-6 F) * 100.
Step 7: Multiply 0.5 by 5, which gives 2.5.
Step 8: Now multiply 2.5 by 10^-6 and then by 100: E = 2.5 * 10^-6 * 100.
Step 9: This simplifies to E = 0.25 * 10^-3 joules, which is equal to 0.25 millijoules (mJ).
