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- Capacitance
NEET · Physics · Capacitance
A parallel plate capacitor with plate area A and separation d has...
A parallel plate capacitor with plate area and separation has an initial capacitance when there is air between the plates. It is then filled with three different dielectric materials. The left half of the space (thickness , full area ) is filled with a dielectric of constant . The right half of the space (thickness ) is divided into two equal parts, each of area , and filled with dielectrics of constants and . The new equivalent capacitance of the system is:
Options
- A
- B
- C
- D
Correct answer
A.
Step-by-step solution
The initial capacitance with air is .
The system can be modeled as a capacitor in series with the parallel combination of capacitors and .
For the left half (thickness , area ):
.
For the right half, it is split into two equal areas () with thickness :
.
.
and are in parallel, so their equivalent capacitance is:
.
Now, is in series with . The total equivalent capacitance is:
.
Answer:
The system can be modeled as a capacitor in series with the parallel combination of capacitors and .
For the left half (thickness , area ):
.
For the right half, it is split into two equal areas () with thickness :
.
.
and are in parallel, so their equivalent capacitance is:
.
Now, is in series with . The total equivalent capacitance is:
.
Answer: