Question

The capacitance of a charged capacitor is \( C \) farad and stored energy is \( U \) joule. Write the expression for charge on the plates of the capacitor.

Hint:

The charge on the plates of a capacitor is related to its capacitance and the energy stored in it through the expression \( Q = \sqrt{2CU} \).

Answer 1

Step 1: Formula for Energy Stored in a Capacitor.
The energy stored in a capacitor is given by the formula: \[ U = \frac{1}{2} C V^2 \] where \( U \) is the energy, \( C \) is the capacitance, and \( V \) is the potential difference across the plates.

Step 2: Relationship Between Charge and Voltage.
The charge \( Q \) on the plates of the capacitor is related to the capacitance and the voltage by the equation: \[ Q = C V \]
Step 3: Substituting Voltage Expression.
From the energy formula \( U = \frac{1}{2} C V^2 \), we can solve for \( V \): \[ V = \sqrt{\frac{2U}{C}} \]
Step 4: Final Expression for Charge.
Substituting this value of \( V \) into the equation for charge: \[ Q = C \times \sqrt{\frac{2U}{C}} = \sqrt{2CU} \]