If the potential difference across a capacitor is doubled, what happens to the s
Practice Questions
Q1
If the potential difference across a capacitor is doubled, what happens to the stored energy?
It doubles
It quadruples
It remains the same
It halves
Questions & Step-by-Step Solutions
If the potential difference across a capacitor is doubled, what happens to the stored energy?
Step 1: Understand that the energy stored in a capacitor is calculated using the formula U = 1/2 C V^2, where U is the energy, C is the capacitance, and V is the voltage (potential difference).
Step 2: Identify what happens when the voltage (V) is doubled. If V becomes 2V, we need to substitute this into the energy formula.
Step 3: Substitute 2V into the formula: U = 1/2 C (2V)^2.
Step 4: Calculate (2V)^2, which equals 4V^2.
Step 5: Now substitute this back into the energy formula: U = 1/2 C (4V^2).
Step 6: Simplify the equation: U = 2 (1/2 C V^2).
Step 7: Notice that 2 (1/2 C V^2) means the energy has doubled, so the stored energy is now 4 times the original energy.
Capacitor Energy Storage – The energy stored in a capacitor is proportional to the square of the voltage across it, as described by the formula U = 1/2 C V^2.
