Capacitors with Dielectric
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359177 Between the plates of a parallel plate condenser, a plate of thickness \({t_1}\) and dielectric constant \({K_1}\) is placed. In the rest of the space, there is another plate of thickness \({t_2}\) and dielectric constant \({K_2}.\) The potential difference across the condenser will be

1 \(\frac{{{\varepsilon _0}Q}}{A}\left( {\frac{{{t_1}}}{{{K_1}}} + \frac{{{t_2}}}{{{K_2}}}} \right)\)
2 \(\frac{Q}{{A{\varepsilon _0}}}\left( {\frac{{{t_1}}}{{{K_1}}} + \frac{{{t_2}}}{{{K_2}}}} \right)\)
3 \(\frac{{{\varepsilon _0}Q}}{A}\left( {{K_1}{t_1} + {K_2}{t_2}} \right)\)
4 \(\frac{Q}{{A{\varepsilon _0}}}\left( {\frac{{{K_1}}}{{{t_1}}} + \frac{{{K_2}}}{{{t_2}}}} \right)\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359178 A parallel plate capacitor is made of two dielectric blocks. One of the blocks has thickness \({d_1}\) and dielectric constant \({K_1}\) and the other has thickness \({d_2}\) and dielectric constant \({K_2}\) as shown in figure. This arrangement can be thought as a dielectric slab of thickness \(\left( {d = {d_1} + {d_2}} \right)\) and effective dielectric constant \(K\). The \(K\) is
supporting img

1 \(\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}\)
2 \(\frac{{{K_1}{K_2}({d_1} + {d_2})}}{{\left( {{K_1}{d_2} + {K_2}{d_1}} \right)}}\)
3 \(\frac{{{K_1}{d_1} + {K_2}{d_2}}}{{{K_1} + {K_2}}}\)
4 \(\frac{{{K_1}{d_1} + {K_2}{d_2}}}{{{d_1} + {d_2}}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359179 The respective radii of the two spheres of a spherical condenser are 12 \(cm\) and 9 \(cm\). The dielectric constant of the medium between them is 3. The capacity of the condenser will be

1 \(120\,pF\)
2 \(240\,mF\)
3 \(240\,F\)
4 \(80\,\mu F\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359180 A parallel plate capacitor has area \(2{m^2}\) separated by 3 dielectric slabs. Their relative permittivity is 2, 3, 6 and thickness is 0.4 \(mm\), 0.6 \(mm\), 1.2 \(mm\) respectively. The capacitance is

1 \(11 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
2 \(5 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
3 \(10 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
4 \(2.95 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359181 Two parallel plates of area \(A\) are separated by two different dielectric as shown in figure. The net capacitance is
supporting img

1 \(\frac{{{\varepsilon _o}A}}{d}\)
2 \(\frac{{3{\varepsilon _o}A}}{{4d}}\)
3 \(\frac{{4{\varepsilon _o}A}}{{3d}}\)
4 \(\frac{{2{\varepsilon _o}A}}{d}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359177 Between the plates of a parallel plate condenser, a plate of thickness \({t_1}\) and dielectric constant \({K_1}\) is placed. In the rest of the space, there is another plate of thickness \({t_2}\) and dielectric constant \({K_2}.\) The potential difference across the condenser will be

1 \(\frac{{{\varepsilon _0}Q}}{A}\left( {\frac{{{t_1}}}{{{K_1}}} + \frac{{{t_2}}}{{{K_2}}}} \right)\)
2 \(\frac{Q}{{A{\varepsilon _0}}}\left( {\frac{{{t_1}}}{{{K_1}}} + \frac{{{t_2}}}{{{K_2}}}} \right)\)
3 \(\frac{{{\varepsilon _0}Q}}{A}\left( {{K_1}{t_1} + {K_2}{t_2}} \right)\)
4 \(\frac{Q}{{A{\varepsilon _0}}}\left( {\frac{{{K_1}}}{{{t_1}}} + \frac{{{K_2}}}{{{t_2}}}} \right)\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359178 A parallel plate capacitor is made of two dielectric blocks. One of the blocks has thickness \({d_1}\) and dielectric constant \({K_1}\) and the other has thickness \({d_2}\) and dielectric constant \({K_2}\) as shown in figure. This arrangement can be thought as a dielectric slab of thickness \(\left( {d = {d_1} + {d_2}} \right)\) and effective dielectric constant \(K\). The \(K\) is
supporting img

1 \(\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}\)
2 \(\frac{{{K_1}{K_2}({d_1} + {d_2})}}{{\left( {{K_1}{d_2} + {K_2}{d_1}} \right)}}\)
3 \(\frac{{{K_1}{d_1} + {K_2}{d_2}}}{{{K_1} + {K_2}}}\)
4 \(\frac{{{K_1}{d_1} + {K_2}{d_2}}}{{{d_1} + {d_2}}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359179 The respective radii of the two spheres of a spherical condenser are 12 \(cm\) and 9 \(cm\). The dielectric constant of the medium between them is 3. The capacity of the condenser will be

1 \(120\,pF\)
2 \(240\,mF\)
3 \(240\,F\)
4 \(80\,\mu F\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359180 A parallel plate capacitor has area \(2{m^2}\) separated by 3 dielectric slabs. Their relative permittivity is 2, 3, 6 and thickness is 0.4 \(mm\), 0.6 \(mm\), 1.2 \(mm\) respectively. The capacitance is

1 \(11 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
2 \(5 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
3 \(10 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
4 \(2.95 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359181 Two parallel plates of area \(A\) are separated by two different dielectric as shown in figure. The net capacitance is
supporting img

1 \(\frac{{{\varepsilon _o}A}}{d}\)
2 \(\frac{{3{\varepsilon _o}A}}{{4d}}\)
3 \(\frac{{4{\varepsilon _o}A}}{{3d}}\)
4 \(\frac{{2{\varepsilon _o}A}}{d}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359177 Between the plates of a parallel plate condenser, a plate of thickness \({t_1}\) and dielectric constant \({K_1}\) is placed. In the rest of the space, there is another plate of thickness \({t_2}\) and dielectric constant \({K_2}.\) The potential difference across the condenser will be

1 \(\frac{{{\varepsilon _0}Q}}{A}\left( {\frac{{{t_1}}}{{{K_1}}} + \frac{{{t_2}}}{{{K_2}}}} \right)\)
2 \(\frac{Q}{{A{\varepsilon _0}}}\left( {\frac{{{t_1}}}{{{K_1}}} + \frac{{{t_2}}}{{{K_2}}}} \right)\)
3 \(\frac{{{\varepsilon _0}Q}}{A}\left( {{K_1}{t_1} + {K_2}{t_2}} \right)\)
4 \(\frac{Q}{{A{\varepsilon _0}}}\left( {\frac{{{K_1}}}{{{t_1}}} + \frac{{{K_2}}}{{{t_2}}}} \right)\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359178 A parallel plate capacitor is made of two dielectric blocks. One of the blocks has thickness \({d_1}\) and dielectric constant \({K_1}\) and the other has thickness \({d_2}\) and dielectric constant \({K_2}\) as shown in figure. This arrangement can be thought as a dielectric slab of thickness \(\left( {d = {d_1} + {d_2}} \right)\) and effective dielectric constant \(K\). The \(K\) is
supporting img

1 \(\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}\)
2 \(\frac{{{K_1}{K_2}({d_1} + {d_2})}}{{\left( {{K_1}{d_2} + {K_2}{d_1}} \right)}}\)
3 \(\frac{{{K_1}{d_1} + {K_2}{d_2}}}{{{K_1} + {K_2}}}\)
4 \(\frac{{{K_1}{d_1} + {K_2}{d_2}}}{{{d_1} + {d_2}}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359179 The respective radii of the two spheres of a spherical condenser are 12 \(cm\) and 9 \(cm\). The dielectric constant of the medium between them is 3. The capacity of the condenser will be

1 \(120\,pF\)
2 \(240\,mF\)
3 \(240\,F\)
4 \(80\,\mu F\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359180 A parallel plate capacitor has area \(2{m^2}\) separated by 3 dielectric slabs. Their relative permittivity is 2, 3, 6 and thickness is 0.4 \(mm\), 0.6 \(mm\), 1.2 \(mm\) respectively. The capacitance is

1 \(11 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
2 \(5 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
3 \(10 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
4 \(2.95 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359181 Two parallel plates of area \(A\) are separated by two different dielectric as shown in figure. The net capacitance is
supporting img

1 \(\frac{{{\varepsilon _o}A}}{d}\)
2 \(\frac{{3{\varepsilon _o}A}}{{4d}}\)
3 \(\frac{{4{\varepsilon _o}A}}{{3d}}\)
4 \(\frac{{2{\varepsilon _o}A}}{d}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359177 Between the plates of a parallel plate condenser, a plate of thickness \({t_1}\) and dielectric constant \({K_1}\) is placed. In the rest of the space, there is another plate of thickness \({t_2}\) and dielectric constant \({K_2}.\) The potential difference across the condenser will be

1 \(\frac{{{\varepsilon _0}Q}}{A}\left( {\frac{{{t_1}}}{{{K_1}}} + \frac{{{t_2}}}{{{K_2}}}} \right)\)
2 \(\frac{Q}{{A{\varepsilon _0}}}\left( {\frac{{{t_1}}}{{{K_1}}} + \frac{{{t_2}}}{{{K_2}}}} \right)\)
3 \(\frac{{{\varepsilon _0}Q}}{A}\left( {{K_1}{t_1} + {K_2}{t_2}} \right)\)
4 \(\frac{Q}{{A{\varepsilon _0}}}\left( {\frac{{{K_1}}}{{{t_1}}} + \frac{{{K_2}}}{{{t_2}}}} \right)\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359178 A parallel plate capacitor is made of two dielectric blocks. One of the blocks has thickness \({d_1}\) and dielectric constant \({K_1}\) and the other has thickness \({d_2}\) and dielectric constant \({K_2}\) as shown in figure. This arrangement can be thought as a dielectric slab of thickness \(\left( {d = {d_1} + {d_2}} \right)\) and effective dielectric constant \(K\). The \(K\) is
supporting img

1 \(\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}\)
2 \(\frac{{{K_1}{K_2}({d_1} + {d_2})}}{{\left( {{K_1}{d_2} + {K_2}{d_1}} \right)}}\)
3 \(\frac{{{K_1}{d_1} + {K_2}{d_2}}}{{{K_1} + {K_2}}}\)
4 \(\frac{{{K_1}{d_1} + {K_2}{d_2}}}{{{d_1} + {d_2}}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359179 The respective radii of the two spheres of a spherical condenser are 12 \(cm\) and 9 \(cm\). The dielectric constant of the medium between them is 3. The capacity of the condenser will be

1 \(120\,pF\)
2 \(240\,mF\)
3 \(240\,F\)
4 \(80\,\mu F\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359180 A parallel plate capacitor has area \(2{m^2}\) separated by 3 dielectric slabs. Their relative permittivity is 2, 3, 6 and thickness is 0.4 \(mm\), 0.6 \(mm\), 1.2 \(mm\) respectively. The capacitance is

1 \(11 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
2 \(5 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
3 \(10 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
4 \(2.95 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359181 Two parallel plates of area \(A\) are separated by two different dielectric as shown in figure. The net capacitance is
supporting img

1 \(\frac{{{\varepsilon _o}A}}{d}\)
2 \(\frac{{3{\varepsilon _o}A}}{{4d}}\)
3 \(\frac{{4{\varepsilon _o}A}}{{3d}}\)
4 \(\frac{{2{\varepsilon _o}A}}{d}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359177 Between the plates of a parallel plate condenser, a plate of thickness \({t_1}\) and dielectric constant \({K_1}\) is placed. In the rest of the space, there is another plate of thickness \({t_2}\) and dielectric constant \({K_2}.\) The potential difference across the condenser will be

1 \(\frac{{{\varepsilon _0}Q}}{A}\left( {\frac{{{t_1}}}{{{K_1}}} + \frac{{{t_2}}}{{{K_2}}}} \right)\)
2 \(\frac{Q}{{A{\varepsilon _0}}}\left( {\frac{{{t_1}}}{{{K_1}}} + \frac{{{t_2}}}{{{K_2}}}} \right)\)
3 \(\frac{{{\varepsilon _0}Q}}{A}\left( {{K_1}{t_1} + {K_2}{t_2}} \right)\)
4 \(\frac{Q}{{A{\varepsilon _0}}}\left( {\frac{{{K_1}}}{{{t_1}}} + \frac{{{K_2}}}{{{t_2}}}} \right)\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359178 A parallel plate capacitor is made of two dielectric blocks. One of the blocks has thickness \({d_1}\) and dielectric constant \({K_1}\) and the other has thickness \({d_2}\) and dielectric constant \({K_2}\) as shown in figure. This arrangement can be thought as a dielectric slab of thickness \(\left( {d = {d_1} + {d_2}} \right)\) and effective dielectric constant \(K\). The \(K\) is
supporting img

1 \(\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}\)
2 \(\frac{{{K_1}{K_2}({d_1} + {d_2})}}{{\left( {{K_1}{d_2} + {K_2}{d_1}} \right)}}\)
3 \(\frac{{{K_1}{d_1} + {K_2}{d_2}}}{{{K_1} + {K_2}}}\)
4 \(\frac{{{K_1}{d_1} + {K_2}{d_2}}}{{{d_1} + {d_2}}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359179 The respective radii of the two spheres of a spherical condenser are 12 \(cm\) and 9 \(cm\). The dielectric constant of the medium between them is 3. The capacity of the condenser will be

1 \(120\,pF\)
2 \(240\,mF\)
3 \(240\,F\)
4 \(80\,\mu F\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359180 A parallel plate capacitor has area \(2{m^2}\) separated by 3 dielectric slabs. Their relative permittivity is 2, 3, 6 and thickness is 0.4 \(mm\), 0.6 \(mm\), 1.2 \(mm\) respectively. The capacitance is

1 \(11 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
2 \(5 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
3 \(10 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
4 \(2.95 \times {10^{ - 8}}\,{\mathop{\rm Farad}\nolimits} \)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359181 Two parallel plates of area \(A\) are separated by two different dielectric as shown in figure. The net capacitance is
supporting img

1 \(\frac{{{\varepsilon _o}A}}{d}\)
2 \(\frac{{3{\varepsilon _o}A}}{{4d}}\)
3 \(\frac{{4{\varepsilon _o}A}}{{3d}}\)
4 \(\frac{{2{\varepsilon _o}A}}{d}\)