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Ray Optics and Optical Instruments — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsRay Optics and Optical Instruments2 Marks
Question
The space between the plates of a parallel plate capacitor is completely filled in two ways. In the first case, it is filled with a slab of dielectric constant K. In the second case, it is filled with two slabs of equal thickness and dielectric constants K1 and K2 respectively as shown in the figure. The capacitance of the capacitor is same in the two cases. Obtain the relationship between K, K1 and K2.

✓

Answer

$\text{C}_1=\frac{\text{K}\varepsilon_0\text{A}}{\text{d}}$
C2 = parallel combination of two capacitors,
$=\frac{\text{K}_1\varepsilon_0\big(\frac{\text{A}}{2}\big)}{\text{d}}+\frac{\text{K}_2\varepsilon_0\big(\frac{\text{A}}{2}\big)}{\text{d}}$
$\frac{\varepsilon_0\text{A}}{2\text{d}}\big(\text{K}_1+\text{K}_2\big)$
$\because\text{C}_1=\text{C}_2$
$\Rightarrow\text{K}=\frac{\text{K}_1+\text{K}_2}{2}$

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