A capacitor is charged to a voltage V and then the voltage is halved. What happe
Practice Questions
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
Questions & Step-by-Step Solutions
A capacitor is charged to a voltage V and then the voltage is halved. What happens to the energy stored in the capacitor?
Correct Answer: Energy becomes one-fourth of the original energy.
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.
Energy Stored in a Capacitor – The energy (U) stored in a capacitor is given by the formula U = 1/2 CV², where C is the capacitance and V is the voltage across the capacitor.
Effect of Voltage on Energy – The energy stored in a capacitor is proportional to the square of the voltage, meaning that if the voltage is halved, the energy decreases by a factor of four.
