Find the value of a capacitor with voltage 5V and 30C.

Analysis

To solve this problem, we need to determine the capacitance ($C$) of a capacitor given the charge ($Q$) stored in it and the potential difference (voltage, $V$) across it.

Concept

The relationship between charge, capacitance, and voltage is defined by the fundamental formula for a capacitor:

Where:

• $Q$ is the charge measured in Coulombs (C).
• $C$ is the capacitance measured in Farads (F).
• $V$ is the potential difference measured in Volts (V).

To find the capacitance, we rearrange the formula to make $C$ the subject:

Step-by-Step Solution

1. Identify the given values: • Charge ($Q$) = $30\text{ C}$ • Voltage ($V$) = $5\text{ V}$

2. Apply the formula: $$C = \frac{30\text{ C}}{5\text{ V}}$$

3. Calculate the result: $$C = 6\text{ F}$$

Conclusion

The calculated capacitance is $6\text{ F}$. This matches option B.

Exam Tip

When dealing with capacitor problems, always remember the triangle method: put $Q$ at the top, and $C$ and $V$ at the bottom. If you need to find $C$, cover it up, and you are left with $Q$ over $V$. This simple trick helps you avoid mistakes under exam pressure!