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Question

A parallel plate capacitor with air as the medium between the plates has a capacitance of 10$$\mu $$ F. The area of the capacitor is divided into two equal halves and filled with two media having dielectric constant $$k_{1}=2$$ and $$k_{2}=4$$. The capacitance will now be :



A
10μ F
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B
20μ F
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C
30μ F
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D
40μ F
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Solution

The correct option is C $$30 \mu $$ F
Initial capacitance is given as $$C=10\mu F$$
$$\Rightarrow C =\dfrac {\varepsilon_0 A}{d}=10\mu F$$
New arrangement acts as two capacitors $$C_1$$ and $$C_2$$ connected in parallel.
Thus capacitance of each part  $$C_1=\dfrac {k_1\varepsilon_0 A_1}{d}$$  and  $$ C_2=\dfrac {k_2 \varepsilon_0 A_2}{d}$$
Equivalent capacitance of parallel combination  $$C_p=C_1+C_2=(k_1+k_2)\dfrac{\epsilon_0(A_1+A_2)}{d}$$ 
$$\implies$$  $$C_p=(k_1+k_2)\dfrac{\epsilon_0 A}{2d}$$       $$(\because A_1 = A_2 = \dfrac{A}{2})$$
Thus $$C_p=(2+4)\times \dfrac{10}{2}=30  \mu F$$

63539_11125_ans_b5a3b4fce9eb4a57a50fae32f3133ad2.png

Physics
NCERT
Standard XII

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