A certain capacitor is charged to a potential difference V. If you wish to increase its stored e

step 1 So we know that the energy in the capacity is nothing but half C square and if fee increasing it

A certain capacitor is charged to a potential difference V....

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Key Concepts

Capacitor Energy Storage

This concept revolves around the idea that a capacitor stores energy in the electric field between its plates. The stored energy is given by the formula E = 1/2 * C * V^2, where C is the capacitance and V is the potential difference across the capacitor. This formula shows that the energy stored is proportional to the square of the voltage applied across the capacitor.

Quadratic Relationship between Voltage and Energy

Because the energy stored in a capacitor depends on the square of the voltage, any change in voltage results in a quadratic change in stored energy. This means that a small percentage change in voltage leads to a larger percentage change in energy. For example, to achieve a specific percentage increase in energy, the required percentage increase in voltage must account for this quadratic relationship.

Percentage Change Calculation

Determining the percentage increase in voltage needed for a specific increase in energy involves equating the new energy to the desired percentage increase of the original energy and solving for the new voltage. Specifically, if the energy is increased by 10%, the new voltage is found by solving V_new^2 = 1.10 * V^2, leading to V_new = V * sqrt(1.10). The percentage increase is then calculated as (sqrt(1.10) - 1) * 100%, which yields the required adjustment.

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