In a parallel plate capacitor, if the distance between the plates is halved, what happens to the capacitance?
Practice Questions
1 question
Q1
In a parallel plate capacitor, if the distance between the plates is halved, what happens to the capacitance?
It halves
It doubles
It remains the same
It quadruples
Capacitance C = ε₀ * A / d. If d is halved, C doubles.
Questions & Step-by-step Solutions
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Q
Q: In a parallel plate capacitor, if the distance between the plates is halved, what happens to the capacitance?
Solution: Capacitance C = ε₀ * A / d. If d is halved, C doubles.
Steps: 7
Step 1: Understand what a parallel plate capacitor is. It consists of two plates separated by a distance.
Step 2: Know the formula for capacitance (C): C = ε₀ * A / d, where ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance between the plates.
Step 3: Identify what happens when the distance (d) is halved. If d becomes d/2, we need to substitute this into the formula.
Step 4: Substitute d/2 into the capacitance formula: C = ε₀ * A / (d/2).
Step 5: Simplify the equation: C = ε₀ * A * (2/d) = 2 * (ε₀ * A / d).
Step 6: Realize that this means the new capacitance is double the original capacitance.
Step 7: Conclude that if the distance between the plates is halved, the capacitance doubles.
