A capacitor is charged to a voltage V and then the voltage is halved. What happens to the energy stored in the capacitor?
Practice Questions
1 question
Q1
A capacitor is charged to a voltage V and then the voltage is halved. What happens to the energy stored in the capacitor?
It doubles
It halves
It remains the same
It becomes zero
The energy stored in a capacitor is proportional to the square of the voltage (U = 1/2 CV²). If the voltage is halved, the energy becomes U/4.
Questions & Step-by-step Solutions
1 item
Q
Q: A capacitor is charged to a voltage V and then the voltage is halved. What happens to the energy stored in the capacitor?
Solution: The energy stored in a capacitor is proportional to the square of the voltage (U = 1/2 CV²). If the voltage is halved, the energy becomes U/4.
Steps: 8
Step 1: Understand that a capacitor stores energy based on the voltage across it.
Step 2: Know the formula for energy stored in a capacitor: U = 1/2 CV², where U is energy, C is capacitance, and V is voltage.
Step 3: If the voltage V is halved, we can express the new voltage as V/2.
Step 4: Substitute V/2 into the energy formula: U' = 1/2 C(V/2)².
Step 5: Calculate (V/2)², which equals V²/4.
Step 6: Now substitute this back into the energy formula: U' = 1/2 C(V²/4).
Step 7: Simplify the equation: U' = (1/2 C V²) / 4 = U/4, where U is the original energy.
Step 8: Conclude that when the voltage is halved, the energy stored in the capacitor becomes one-fourth of the original energy.
