Topic: Capacitors, series and parallel combination, parallel plate capacitor with/without dielectric· Electrostatics
A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k_1,k_2,k_3 and k_4 as shown in the figure below. If a single dielectric material is to be used to have th…
A parallel-plate capacitor of area \(A\), plate separation \(d\) and capacitance \(C\) is filled with four dielectric materials having dielectric constants \(k_1,k_2,k_3\) and \(k_4\) as shown in the figure below. If a single dielectric material is to be used to have the same capacitance \(C\) in this capacitor, then its dielectric constant \(k\) is given by
1. \(k=\frac{2}{3}(k_1+k_2+k_3)+2k_4\)
2. \(\frac{2}{k}=\frac{3}{k_1+k_2+k_3}+\frac{1}{k_4}\)
3. \(\frac{1}{k}=\frac{1}{k_1}+\frac{1}{k_2}+\frac{1}{k_3}+\frac{3}{2k_4}\)
4. \(k=k_1+k_2+k_3+3k_4\)