Question

If the charge on a capacitor is increased by $2\ \text{C}$, the energy stored in it increases by $21\%$. The total original charge on the capacitor is

• A. $10\ \text{C}$
• B. $5\ \text{C}$
• C. $20\ \text{C}$
• D. $15\ \text{C}$

Hint:

Whenever a problem states that a squared quantity increases by $21\%$, remember that its base variable must increase by exactly $10\%$ (since $1.1^2 = 1.21$). Therefore, the $2\ \text{C}$ addition represents exactly $10\%$ of the original charge: $0.10 \times Q = 2 \implies Q = 20\ \text{C}$. This relationship can be worked out mentally in under five seconds!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
A squared quantity increases by 21%. Determine the original base quantity from a given absolute change.

Step 2: Key Formula or Approach:
A 21% increase in a squared variable means (x + Δx)²/x² = 1.21. Since 1.1² = 1.21, the base variable increased by exactly 10%.

Step 3: Detailed Explanation:
The 2 C addition therefore represents precisely 10% of the original charge: 0.10 × Q = 2 → Q = 20 C. This inverse reasoning—from percentage increase of a square back to the linear percentage change—uses the perfect square 1.1² = 1.21 and can be executed mentally in seconds without setting up a quadratic equation.

Step 4: Final Answer:
The original charge Q equals 20 C.