Capacitors in parallel:
Give as clear as explanation as possible as to why it is physically reasonable to expect that two identical parallel plate capacitors are placed in parallel ought to have twice the capacitance as one capacitor.
I did my best earlier.
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To understand why two identical parallel plate capacitors placed in parallel have twice the capacitance, let's first review how capacitors store charge.
A capacitor consists of two parallel plates separated by a dielectric material. When a voltage is applied across the plates, positive charge accumulates on one plate while an equal amount of negative charge accumulates on the other plate. The electric field created between the plates causes the charges to be attracted and stored, resulting in the potential energy of the capacitor.
Now, when two identical capacitors are placed in parallel, their plates are connected together such that the positive plates are connected and the negative plates are connected. This effectively creates a larger capacitor with twice the plate area compared to a single capacitor.
The key concept to understand here is that the capacitance of a capacitor depends on the plate area. With a larger plate area, the parallel combination of the two capacitors increases the amount of charge that can be stored for a given voltage. Thus, the total charge stored in the parallel combination is twice that of a single capacitor.
Mathematically, the capacitance (C) of a parallel plate capacitor is directly proportional to the plate area (A) and inversely proportional to the distance between the plates (d). The formula for capacitance is given by C = ε₀ * (A/d), where ε₀ is the permittivity of free space.
Since the two capacitors in parallel share the same distance between the plates, the combined capacitance (C_total) can be calculated by adding the capacitances of the individual capacitors.
C_total = C1 + C2 = (ε₀ * (A/d)) + (ε₀ * (A/d)) = 2 * (ε₀ * (A/d))
Therefore, the combined capacitance is twice that of a single capacitor, as expected.
In conclusion, when two identical parallel plate capacitors are placed in parallel, the effective plate area is doubled, resulting in twice the capacitance. This allows the combined capacitors to store more charge for a given voltage.