Capacitors with Dielectric
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359203 A parallel-plate capacitor of area \(A\), plate separation d and capacitance \(C\) is filled with four dielectric materials having dielectric constants \({K_1},{K_2},{K_3}\,{\mathop{\rm and}\nolimits} \,{K_4}\) as shown in the figure. 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
supporting img

1 \(K = {K_1} + {K_2} + {K_3} + 3{K_4}\)
2 \(K = \frac{2}{3}\left( {{K_1} + {K_2} + {K_3}} \right) + 2{K_4}\)
3 \(\frac{2}{K} = \frac{3}{{{K_1} + {K_2} + {K_3}}} + \frac{1}{{{K_4}}}\)
4 \(K = \frac{2}{3}\left[ {\frac{{{K_1}{K_4}}}{{{K_1} + {K_4}}} + \frac{{{K_2}{K_4}}}{{{K_2} + {K_4}}} + \frac{{{K_3}{K_4}}}{{{K_3} + {K_4}}}} \right]\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359204 A parallel plate condenser is filled with two dielectric as shown. Area of each plate is \(A\) and the separation is \(t\). The dielectric constants are \({k_1}\) and \({k_2}\) respectively. Its capacitance in farad will be
supporting img

1 \(\frac{{{\varepsilon _o}A}}{t} \cdot \frac{{{k_1} - {k_2}}}{2}\)
2 \(\frac{{{\varepsilon _o}A}}{t}({k_1} + {k_2})\)
3 \(\frac{{{\varepsilon _o}A}}{t}\frac{{{k_1} + {k_2}}}{2}\)
4 \(\frac{{2{\varepsilon _o}A}}{t}({k_1} + {k_2})\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359205 A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (\(U\)) as \(\varepsilon = \alpha U\) where \(\alpha = 2{V^{ - 1}}\). A similar capacitor with no dielectric is charged to \({U_0} = 18V.\) It is then connected to the uncharged capacitor with the dielectric. The final voltage on the capacitors

1 \(5V\)
2 \(6V\)
3 \(7V\)
4 \(8V\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359206 An uncharged capacitor with a solid dielectric is connecetd to a similar air capacitor charged to a potential of \({V_0}\). If the common potential after sharing of charges becomes \(V\), then the dielectric constant of the solid dielectric must be

1 \(\frac{V}{{{V_0}}}\)
2 \(\frac{{{V_0}}}{V}\)
3 \(\frac{{{V_0} - V}}{V}\)
4 \(\frac{{\left( {{V_0} + V} \right)}}{V}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359203 A parallel-plate capacitor of area \(A\), plate separation d and capacitance \(C\) is filled with four dielectric materials having dielectric constants \({K_1},{K_2},{K_3}\,{\mathop{\rm and}\nolimits} \,{K_4}\) as shown in the figure. 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
supporting img

1 \(K = {K_1} + {K_2} + {K_3} + 3{K_4}\)
2 \(K = \frac{2}{3}\left( {{K_1} + {K_2} + {K_3}} \right) + 2{K_4}\)
3 \(\frac{2}{K} = \frac{3}{{{K_1} + {K_2} + {K_3}}} + \frac{1}{{{K_4}}}\)
4 \(K = \frac{2}{3}\left[ {\frac{{{K_1}{K_4}}}{{{K_1} + {K_4}}} + \frac{{{K_2}{K_4}}}{{{K_2} + {K_4}}} + \frac{{{K_3}{K_4}}}{{{K_3} + {K_4}}}} \right]\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359204 A parallel plate condenser is filled with two dielectric as shown. Area of each plate is \(A\) and the separation is \(t\). The dielectric constants are \({k_1}\) and \({k_2}\) respectively. Its capacitance in farad will be
supporting img

1 \(\frac{{{\varepsilon _o}A}}{t} \cdot \frac{{{k_1} - {k_2}}}{2}\)
2 \(\frac{{{\varepsilon _o}A}}{t}({k_1} + {k_2})\)
3 \(\frac{{{\varepsilon _o}A}}{t}\frac{{{k_1} + {k_2}}}{2}\)
4 \(\frac{{2{\varepsilon _o}A}}{t}({k_1} + {k_2})\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359205 A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (\(U\)) as \(\varepsilon = \alpha U\) where \(\alpha = 2{V^{ - 1}}\). A similar capacitor with no dielectric is charged to \({U_0} = 18V.\) It is then connected to the uncharged capacitor with the dielectric. The final voltage on the capacitors

1 \(5V\)
2 \(6V\)
3 \(7V\)
4 \(8V\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359206 An uncharged capacitor with a solid dielectric is connecetd to a similar air capacitor charged to a potential of \({V_0}\). If the common potential after sharing of charges becomes \(V\), then the dielectric constant of the solid dielectric must be

1 \(\frac{V}{{{V_0}}}\)
2 \(\frac{{{V_0}}}{V}\)
3 \(\frac{{{V_0} - V}}{V}\)
4 \(\frac{{\left( {{V_0} + V} \right)}}{V}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359203 A parallel-plate capacitor of area \(A\), plate separation d and capacitance \(C\) is filled with four dielectric materials having dielectric constants \({K_1},{K_2},{K_3}\,{\mathop{\rm and}\nolimits} \,{K_4}\) as shown in the figure. 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
supporting img

1 \(K = {K_1} + {K_2} + {K_3} + 3{K_4}\)
2 \(K = \frac{2}{3}\left( {{K_1} + {K_2} + {K_3}} \right) + 2{K_4}\)
3 \(\frac{2}{K} = \frac{3}{{{K_1} + {K_2} + {K_3}}} + \frac{1}{{{K_4}}}\)
4 \(K = \frac{2}{3}\left[ {\frac{{{K_1}{K_4}}}{{{K_1} + {K_4}}} + \frac{{{K_2}{K_4}}}{{{K_2} + {K_4}}} + \frac{{{K_3}{K_4}}}{{{K_3} + {K_4}}}} \right]\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359204 A parallel plate condenser is filled with two dielectric as shown. Area of each plate is \(A\) and the separation is \(t\). The dielectric constants are \({k_1}\) and \({k_2}\) respectively. Its capacitance in farad will be
supporting img

1 \(\frac{{{\varepsilon _o}A}}{t} \cdot \frac{{{k_1} - {k_2}}}{2}\)
2 \(\frac{{{\varepsilon _o}A}}{t}({k_1} + {k_2})\)
3 \(\frac{{{\varepsilon _o}A}}{t}\frac{{{k_1} + {k_2}}}{2}\)
4 \(\frac{{2{\varepsilon _o}A}}{t}({k_1} + {k_2})\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359205 A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (\(U\)) as \(\varepsilon = \alpha U\) where \(\alpha = 2{V^{ - 1}}\). A similar capacitor with no dielectric is charged to \({U_0} = 18V.\) It is then connected to the uncharged capacitor with the dielectric. The final voltage on the capacitors

1 \(5V\)
2 \(6V\)
3 \(7V\)
4 \(8V\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359206 An uncharged capacitor with a solid dielectric is connecetd to a similar air capacitor charged to a potential of \({V_0}\). If the common potential after sharing of charges becomes \(V\), then the dielectric constant of the solid dielectric must be

1 \(\frac{V}{{{V_0}}}\)
2 \(\frac{{{V_0}}}{V}\)
3 \(\frac{{{V_0} - V}}{V}\)
4 \(\frac{{\left( {{V_0} + V} \right)}}{V}\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359203 A parallel-plate capacitor of area \(A\), plate separation d and capacitance \(C\) is filled with four dielectric materials having dielectric constants \({K_1},{K_2},{K_3}\,{\mathop{\rm and}\nolimits} \,{K_4}\) as shown in the figure. 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
supporting img

1 \(K = {K_1} + {K_2} + {K_3} + 3{K_4}\)
2 \(K = \frac{2}{3}\left( {{K_1} + {K_2} + {K_3}} \right) + 2{K_4}\)
3 \(\frac{2}{K} = \frac{3}{{{K_1} + {K_2} + {K_3}}} + \frac{1}{{{K_4}}}\)
4 \(K = \frac{2}{3}\left[ {\frac{{{K_1}{K_4}}}{{{K_1} + {K_4}}} + \frac{{{K_2}{K_4}}}{{{K_2} + {K_4}}} + \frac{{{K_3}{K_4}}}{{{K_3} + {K_4}}}} \right]\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359204 A parallel plate condenser is filled with two dielectric as shown. Area of each plate is \(A\) and the separation is \(t\). The dielectric constants are \({k_1}\) and \({k_2}\) respectively. Its capacitance in farad will be
supporting img

1 \(\frac{{{\varepsilon _o}A}}{t} \cdot \frac{{{k_1} - {k_2}}}{2}\)
2 \(\frac{{{\varepsilon _o}A}}{t}({k_1} + {k_2})\)
3 \(\frac{{{\varepsilon _o}A}}{t}\frac{{{k_1} + {k_2}}}{2}\)
4 \(\frac{{2{\varepsilon _o}A}}{t}({k_1} + {k_2})\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359205 A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (\(U\)) as \(\varepsilon = \alpha U\) where \(\alpha = 2{V^{ - 1}}\). A similar capacitor with no dielectric is charged to \({U_0} = 18V.\) It is then connected to the uncharged capacitor with the dielectric. The final voltage on the capacitors

1 \(5V\)
2 \(6V\)
3 \(7V\)
4 \(8V\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359206 An uncharged capacitor with a solid dielectric is connecetd to a similar air capacitor charged to a potential of \({V_0}\). If the common potential after sharing of charges becomes \(V\), then the dielectric constant of the solid dielectric must be

1 \(\frac{V}{{{V_0}}}\)
2 \(\frac{{{V_0}}}{V}\)
3 \(\frac{{{V_0} - V}}{V}\)
4 \(\frac{{\left( {{V_0} + V} \right)}}{V}\)