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BITSAT 2017
Exam
BITSAT
Year
2017
Subject
Physics
Chapter
Capacitance

BITSAT 2017 · Physics · Capacitance

A parallel plate capacitor with air between the plates has a...

A parallel plate capacitor with air between the plates has a capacitance of 9pF9pF. The separation between the plates is dd. The space between the plates is now filled with two dielectrics constant K1=3{K}_{1} = 3 and thickness d3\dfrac{d}{3} while the other one has dielectric constant K2=6{K}_{2} = 6 and thickness 2d3\dfrac{2d}{3}. Capacitance of the capacitor is now&A parallel plate capacitor with air between the plates has a capacitance of 9pF . The separation between the plates is

Options

  1. A1.8pF1. 8pF
  2. B45pF45pF
  3. C40.5pF40. 5pF
  4. D20.25pF20. 25pF

Correct answer

C. 40.5pF40. 5pF

Step-by-step solution

The two capacitors formed are in parallel, hence capacitance of the combination

C=C1C2C1+C2...(i)C = \dfrac{{C}_{1}{C}_{2}}{{C}_{1} + {C}_{2}}... ( i )

where, C1=K1ε0Ad3(∵C=ε0Ad)...(ii){C}_{1} = \dfrac{{K}_{1}{ε}_{0}A}{d3} \left(∵ C = \dfrac{{ε}_{0}A}{d}\right)... ( ii )

C2=K2ε0A2d3...(iii){C}_{2} = \dfrac{{K}_{2}{ε}_{0}A}{2d3}... ( iii )

Ceq=3K1ε0Ad×K2ε0A⋅32d3K1ε0Ad+3K2ε0A2d{C}_{eq} = \dfrac{\dfrac{3{K}_{1}{ε}_{0}A}{d} \times \dfrac{{K}_{2}{ε}_{0}A \cdot 3}{2d}}{\dfrac{3{K}_{1}{ε}_{0}A}{d} + \dfrac{3{K}_{2}{ε}_{0}A}{2d}}

=9K1K2ε02A22d2×dε0A×18= \dfrac{9{K}_{1}{K}_{2}{ε}_{0}^{2}A^{2}}{2d^{2}} \times \dfrac{d}{{ε}_{0}A \times 18}

It is given

A parallel plate capacitor with air between the plates has a capacitance of 9pF . The separation between the plates is

ε0Ad=9pF\dfrac{{ε}_{0}A}{d} = 9pF

Using given values

Ceq=40.5pF{C}_{eq} = 40. 5pF

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