Question

Two capacitors \(C_1\) and \(C_2\) are charged to \(100\,V\) and \(120\,V\) respectively. It is found that upon connecting them together in parallel, the potential on each one of them is zero. Therefore

• A. \(C_1 + 3C_2 = 0\)
• B. \(5C_1 = 3C_2\)
• C. \(5C_1 + 6C_2 = 0\)
• D. \(5C_1 = -6C_2\)

Hint:

If final potential becomes zero, total charge must cancel out. Use \(Q = CV\).

Answer 1

The Correct Option is D

Step 1: Charge on capacitors.
\[ Q_1 = C_1 \cdot 100, \quad Q_2 = C_2 \cdot 120 \]

Step 2: Final potential is zero.
After connection, net charge becomes zero.
\[ Q_1 + Q_2 = 0 \]

Step 3: Substitute charges.
\[ 100C_1 + 120C_2 = 0 \]

Step 4: Simplify equation.
\[ 5C_1 + 6C_2 = 0 \]

Step 5: Rearranging.
\[ 5C_1 = -6C_2 \]

Step 6: Final conclusion.
\[ \boxed{5C_1 = -6C_2} \] Hence, correct answer is option (D).