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JIPMER 2013
Exam
JIPMER
Year
2013
Subject
Physics
Chapter
Capacitance

JIPMER 2013 · Physics · Capacitance

A parallel plate condenser is filled with two dielectrics as shown...

A parallel plate condenser is filled with two dielectrics as shown in figure. Area of each pate is A m2A \mathrm{~m}^2 and the separation is dd metre. The dielectric constants are K1K_1 and K2K_2 respectively. Its capacitance in farad will be A parallel plate condenser is filled with two dielectrics as shown in figure. Area of each pate is A ~m^2 and the

Options

  1. A2ε0Ad(K1+K2K1K2)\frac{2 \varepsilon_0 A}{d}\left(\frac{K_1+K_2}{K_1 K_2}\right)
  2. B2ε0Ad(K1K2K1+K2)\frac{2 \varepsilon_0 A}{d}\left(\frac{K_1 K_2}{K_1+K_2}\right)
  3. Cε0Ad(K1+K22K1K2)\frac{\varepsilon_0 A}{d}\left(\frac{K_1+K_2}{2 K_1 K_2}\right)
  4. D\frac{\varepsilon_0 A K_1 K_2}{2\left(d_2 K_1+d_1 K_2\right)}

Correct answer

B. 2ε0Ad(K1K2K1+K2)\frac{2 \varepsilon_0 A}{d}\left(\frac{K_1 K_2}{K_1+K_2}\right)

Step-by-step solution

From the formula C=ε0A1k1+1k2=ε0At(k1k2k1+k2)=2ε0Ad(k1k2k1+k2)\begin{aligned} C & =\frac{\varepsilon_0 A}{\frac{1}{k_1}+\frac{1}{k_2}}=\frac{\varepsilon_0 A}{t}\left(\frac{k_1 k_2}{k_1+k_2}\right) \\ & =\frac{2 \varepsilon_0 A}{d}\left(\frac{k_1 k_2}{k_1+k_2}\right)\end{aligned}
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