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What happens to the energy stored in a capacitor if the voltage across it is dou
What happens to the energy stored in a capacitor if the voltage across it is doubled?
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What happens to the energy stored in a capacitor if the voltage across it is doubled?
It doubles
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The energy stored in a capacitor is given by U = 1/2 C V². If the voltage is doubled, the energy increases by a factor of four.
Questions & Step-by-step Solutions
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Q
Q: What happens to the energy stored in a capacitor if the voltage across it is doubled?
Solution:
The energy stored in a capacitor is given by U = 1/2 C V². If the voltage is doubled, the energy increases by a factor of four.
Steps: 7
Show Steps
Step 1: Understand the formula for energy stored in a capacitor, which is U = 1/2 C V².
Step 2: Identify what happens when the voltage (V) is doubled. If the original voltage is V, the new voltage becomes 2V.
Step 3: Substitute the new voltage into the energy formula: U = 1/2 C (2V)².
Step 4: Calculate (2V)², which equals 4V².
Step 5: Now the energy formula becomes U = 1/2 C (4V²).
Step 6: Simplify the formula: U = 2 C V², which shows that the energy is now four times the original energy.
Step 7: Conclude that when the voltage is doubled, the energy stored in the capacitor increases by a factor of four.
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