If the charge on a capacitor is doubled, what happens to the energy stored? (201

If the charge on a capacitor is doubled, what happens to the energy stored? (2019)

If the charge on a capacitor is doubled, what happens to the energy stored? (2019)

Step 1: Understand that a capacitor stores energy based on its charge.
Step 2: Know the formula for energy stored in a capacitor: U = Q^2 / (2C), where U is energy, Q is charge, and C is capacitance.
Step 3: If the charge (Q) is doubled, it becomes 2Q.
Step 4: Substitute 2Q into the energy formula: U = (2Q)^2 / (2C).
Step 5: Calculate (2Q)^2, which equals 4Q^2.
Step 6: Now the formula looks like this: U = 4Q^2 / (2C).
Step 7: Simplify the equation: U = 2Q^2 / C.
Step 8: Compare the new energy (2Q^2 / C) to the original energy (Q^2 / (2C)).
Step 9: Notice that the new energy is 4 times the original energy.
Step 10: Conclude that doubling the charge increases the energy stored by a factor of 4.

Energy Stored in a Capacitor – The energy (U) stored in a capacitor is given by the formula U = Q^2/(2C), where Q is the charge and C is the capacitance.
Proportional Relationships – Understanding how changes in charge affect energy, specifically that energy is proportional to the square of the charge.