Calculating Capacitor Capacitance from Charge and Voltage

A capacitor is a device that stores electrical energy in an electric field. Its ability to store charge is measured by its capacitance. Capacitance depends on the physical characteristics of the capacitor, such as the size, shape, and separation of the conductors, and the material between them.

The relationship between the charge (Q) stored on a capacitor, the voltage (V) across it, and its capacitance (C) is given by a fundamental formula in electrostatics.

Understanding the Capacitor Formula

The formula connecting these three quantities is:

\( Q = C \times V \)

Where:

• \( Q \) is the charge stored in Coulombs (C).
• \( C \) is the capacitance in Farads (F).
• \( V \) is the voltage across the capacitor in Volts (V).

We are given the charge \( Q = 0.5 \) Coulomb and the voltage \( V = 10 \) Volt. We need to find the capacitance \( C \).

Step-by-Step Calculation

To find the capacitance \( C \), we can rearrange the formula \( Q = C \times V \) to solve for \( C \):

\( C = \frac{Q}{V} \)

Now, we substitute the given values into this rearranged formula:

\( C = \frac{0.5 \text{ C}}{10 \text{ V}} \)

Performing the division:

\( C = 0.05 \text{ Farad} \)

Result

The value of the capacitance of the capacitor is \( 0.05 \) Farad. This means that for every volt of potential difference across the capacitor, it stores \( 0.05 \) Coulombs of charge.

Comparing our calculated value with the given options, we find that \( 0.05 \) Farad matches one of the choices.