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Choose the correct relation:...

Choose the correct relation:

A

`q=V//C`

B

`C=Vxxq`

C

`V=q//c`

D

`V=cq`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to identify the correct relation among the given options related to a capacitor. The relevant quantities are charge (q), potential difference (v), and capacitance (c). ### Step-by-Step Solution: 1. **Understand the Definitions**: - **Charge (q)**: The amount of electric charge stored in the capacitor. - **Potential Difference (v)**: The voltage across the capacitor. - **Capacitance (c)**: The ability of a capacitor to store charge per unit voltage, defined as \( c = \frac{q}{v} \). 2. **Recall the Fundamental Relation**: - The fundamental relation that connects these three quantities is given by: \[ q = cv \] - This means that the charge (q) stored in a capacitor is equal to the capacitance (c) multiplied by the potential difference (v). 3. **Rearranging the Equation**: - From the relation \( q = cv \), we can rearrange it to express potential difference (v) in terms of charge (q) and capacitance (c): \[ v = \frac{q}{c} \] - This shows that the potential difference is directly proportional to the charge and inversely proportional to the capacitance. 4. **Analyzing the Given Options**: - Now, let's analyze the provided options: - Option 1: \( q = \frac{v}{c} \) (Incorrect) - Option 2: \( c = vq \) (Incorrect) - Option 3: \( v = \frac{q}{c} \) (Correct) - Option 4: \( v = cq \) (Incorrect) 5. **Conclusion**: - The correct relation among the given options is: \[ v = \frac{q}{c} \] - Therefore, the correct option is **Option 3**.

To solve the problem, we need to identify the correct relation among the given options related to a capacitor. The relevant quantities are charge (q), potential difference (v), and capacitance (c). ### Step-by-Step Solution: 1. **Understand the Definitions**: - **Charge (q)**: The amount of electric charge stored in the capacitor. - **Potential Difference (v)**: The voltage across the capacitor. - **Capacitance (c)**: The ability of a capacitor to store charge per unit voltage, defined as \( c = \frac{q}{v} \). ...
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