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In a parallel-plate capacitor, how can the capacitance be decreased?
- a)Increasing the stored charge in the capacitor
- b)Decreasing the stored charge in the capacitor
- c)Decreasing the gap between the charged plates
- d)Increasing the gap between the charged plates
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In a parallel-plate capacitor, how can the capacitance be decreased?a)...
- Recall the capacitance formula for a parallel plate capacitor.
- The formula is C = ε0A/d, with A being the surface area of one of the plates and d being the distance between two plates. Note that capacitance can be inferred purely from geometric properties of the capacitor.
- Increasing the gap between in charged plates will decrease the capacitance.
Community Answer
In a parallel-plate capacitor, how can the capacitance be decreased?a)...
Decreasing the gap between the charged plates is the correct answer to decrease the capacitance of a parallel-plate capacitor. This can be explained by considering the formula for the capacitance of a parallel-plate capacitor, which is given by:
C = ε₀A/d
where C is the capacitance, ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance (gap) between the plates.
Explanation:
1. Capacitance Formula:
The capacitance of a parallel-plate capacitor is directly proportional to the area of the plates (A) and inversely proportional to the distance between the plates (d).
2. Decreasing the Gap:
By decreasing the gap between the charged plates, the distance (d) in the capacitance formula becomes smaller. As a result, the capacitance of the capacitor decreases.
3. Effect on Electric Field:
When the gap between the plates is decreased, the electric field between the plates becomes stronger. This is because the electric field is equal to the voltage (V) across the capacitor divided by the distance (d) between the plates:
E = V/d
If the voltage remains constant and the distance decreases, the electric field increases. This stronger electric field leads to a decrease in the capacitance.
4. Increased Overlapping Area:
When the gap between the plates is decreased, the overlapping area (A) of the plates increases. This increased overlapping area allows for more charge to be stored on the plates. However, the increase in charge is proportionally smaller than the decrease in distance, resulting in a decrease in capacitance.
Conclusion:
By decreasing the gap between the charged plates in a parallel-plate capacitor, the capacitance can be decreased. This is because the capacitance is inversely proportional to the distance between the plates. Decreasing the gap increases the electric field and allows for increased charge storage, but the decrease in distance dominates, resulting in a lower capacitance.
C = ε₀A/d
where C is the capacitance, ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance (gap) between the plates.
Explanation:
1. Capacitance Formula:
The capacitance of a parallel-plate capacitor is directly proportional to the area of the plates (A) and inversely proportional to the distance between the plates (d).
2. Decreasing the Gap:
By decreasing the gap between the charged plates, the distance (d) in the capacitance formula becomes smaller. As a result, the capacitance of the capacitor decreases.
3. Effect on Electric Field:
When the gap between the plates is decreased, the electric field between the plates becomes stronger. This is because the electric field is equal to the voltage (V) across the capacitor divided by the distance (d) between the plates:
E = V/d
If the voltage remains constant and the distance decreases, the electric field increases. This stronger electric field leads to a decrease in the capacitance.
4. Increased Overlapping Area:
When the gap between the plates is decreased, the overlapping area (A) of the plates increases. This increased overlapping area allows for more charge to be stored on the plates. However, the increase in charge is proportionally smaller than the decrease in distance, resulting in a decrease in capacitance.
Conclusion:
By decreasing the gap between the charged plates in a parallel-plate capacitor, the capacitance can be decreased. This is because the capacitance is inversely proportional to the distance between the plates. Decreasing the gap increases the electric field and allows for increased charge storage, but the decrease in distance dominates, resulting in a lower capacitance.
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In a parallel-plate capacitor, how can the capacitance be decreased?a)Increasing the stored charge in the capacitorb)Decreasing the stored charge in the capacitorc)Decreasing the gap between the charged platesd)Increasing the gap between the charged platesCorrect answer is option 'D'. Can you explain this answer?
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