CAPACITANCE
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Electrostatic Potentials and Capacitance

268109 The area of the positive plate is \(A_{1}\) and the area of the negative plate is \(A_{2}\left(A_{2}\lt A_{1}\right)\). They are parallel to each other and are separated by a distanced. The capacity of a condenser with air as dielectric is

1 \(\frac{\varepsilon_{0} A_{1}}{d}\)
2 \(\frac{\varepsilon_{0} A_{2}}{d}\)
3 \(\frac{\varepsilon_{0} A_{1} A_{2}}{d}\)
4 \(\frac{\varepsilon_{0} A_{1}}{A_{2} d}\)
Electrostatic Potentials and Capacitance

268110 The cross section of a cable is shown in fig. The inner conductor has a radius of \(10 \mathrm{~mm}\) and the dielectric has a thickness of \(5 \mathrm{~mm}\). The cable is \(8 \mathrm{~km}\) long. Then the capacitance of the cable is \(\left[\log _{e} 1.5=0.4\right]\)

1 \(3.8 \mu \mathrm{F}\)\(\mathrm{F}\)
2 \(1.1 \mu \mathrm{F}\)
3 \(4.8 \times 10^{-10} \mu \mathrm{F}\)
4 \(3.3 \mu \mathrm{F}\)
Electrostatic Potentials and Capacitance

268121 The capacity of a condenser \(\mathrm{A}\) is \(10 \mu \mathrm{F}\) and it is charged to a battery of 100 volt. The battery is disconnected and the condenser A is connected to a condenser B the common potential is \(40 \mathrm{~V}\). The capacity of \(B\) is

1 \(8 \mu \mathrm{F}\)
2 \(15 \mu \mathrm{F}\)
3 \(2 \mu \mathrm{F}\)
4 \(1 \mu F\)
Electrostatic Potentials and Capacitance

268122 A parallel plate capacitor has the space between its plates filled by two slabs of thickness \(\frac{d}{2}\) each and dielectric constant \(K_{1}\) and \(K_{2}\). d is the plate separation of the capacitor. The capacitance of the capacitor is

1 \(\frac{2 \varepsilon_{0} A}{d}\left(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\right)\)
2 \(\frac{2 \varepsilon_{0} A}{d}\left(K_{1}+K_{2}\right)\)
3 \(\frac{2 \varepsilon_{0} A}{d}\left(\frac{K_{1} K_{2}}{K_{1}+K_{2}}\right)\)
4 \(\frac{2 \varepsilon_{0} d}{A}\left(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\right)\)
Electrostatic Potentials and Capacitance

268123 An isolated capacitor of capacitance ' \(C\) ' is charged to a potential ' \(V\) '. Then a dielectric slab of dielectric constant \(\mathrm{K}\) is inserted as shown in fig. The net charge on four surfaces \(1,2,3\) and 4 would be respectively.

1 \(0, C V,-C V, 0\)
2 \(0, \frac{C V}{K}, \frac{-C V}{K}, 0\)
3 \(\mathrm{CV}, 0,0,-\mathrm{CV}\)
4 \(C V, \frac{-C V}{K}, \frac{C V}{K},-C V\)
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Electrostatic Potentials and Capacitance

268109 The area of the positive plate is \(A_{1}\) and the area of the negative plate is \(A_{2}\left(A_{2}\lt A_{1}\right)\). They are parallel to each other and are separated by a distanced. The capacity of a condenser with air as dielectric is

1 \(\frac{\varepsilon_{0} A_{1}}{d}\)
2 \(\frac{\varepsilon_{0} A_{2}}{d}\)
3 \(\frac{\varepsilon_{0} A_{1} A_{2}}{d}\)
4 \(\frac{\varepsilon_{0} A_{1}}{A_{2} d}\)
Electrostatic Potentials and Capacitance

268110 The cross section of a cable is shown in fig. The inner conductor has a radius of \(10 \mathrm{~mm}\) and the dielectric has a thickness of \(5 \mathrm{~mm}\). The cable is \(8 \mathrm{~km}\) long. Then the capacitance of the cable is \(\left[\log _{e} 1.5=0.4\right]\)

1 \(3.8 \mu \mathrm{F}\)\(\mathrm{F}\)
2 \(1.1 \mu \mathrm{F}\)
3 \(4.8 \times 10^{-10} \mu \mathrm{F}\)
4 \(3.3 \mu \mathrm{F}\)
Electrostatic Potentials and Capacitance

268121 The capacity of a condenser \(\mathrm{A}\) is \(10 \mu \mathrm{F}\) and it is charged to a battery of 100 volt. The battery is disconnected and the condenser A is connected to a condenser B the common potential is \(40 \mathrm{~V}\). The capacity of \(B\) is

1 \(8 \mu \mathrm{F}\)
2 \(15 \mu \mathrm{F}\)
3 \(2 \mu \mathrm{F}\)
4 \(1 \mu F\)
Electrostatic Potentials and Capacitance

268122 A parallel plate capacitor has the space between its plates filled by two slabs of thickness \(\frac{d}{2}\) each and dielectric constant \(K_{1}\) and \(K_{2}\). d is the plate separation of the capacitor. The capacitance of the capacitor is

1 \(\frac{2 \varepsilon_{0} A}{d}\left(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\right)\)
2 \(\frac{2 \varepsilon_{0} A}{d}\left(K_{1}+K_{2}\right)\)
3 \(\frac{2 \varepsilon_{0} A}{d}\left(\frac{K_{1} K_{2}}{K_{1}+K_{2}}\right)\)
4 \(\frac{2 \varepsilon_{0} d}{A}\left(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\right)\)
Electrostatic Potentials and Capacitance

268123 An isolated capacitor of capacitance ' \(C\) ' is charged to a potential ' \(V\) '. Then a dielectric slab of dielectric constant \(\mathrm{K}\) is inserted as shown in fig. The net charge on four surfaces \(1,2,3\) and 4 would be respectively.

1 \(0, C V,-C V, 0\)
2 \(0, \frac{C V}{K}, \frac{-C V}{K}, 0\)
3 \(\mathrm{CV}, 0,0,-\mathrm{CV}\)
4 \(C V, \frac{-C V}{K}, \frac{C V}{K},-C V\)
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Electrostatic Potentials and Capacitance

268109 The area of the positive plate is \(A_{1}\) and the area of the negative plate is \(A_{2}\left(A_{2}\lt A_{1}\right)\). They are parallel to each other and are separated by a distanced. The capacity of a condenser with air as dielectric is

1 \(\frac{\varepsilon_{0} A_{1}}{d}\)
2 \(\frac{\varepsilon_{0} A_{2}}{d}\)
3 \(\frac{\varepsilon_{0} A_{1} A_{2}}{d}\)
4 \(\frac{\varepsilon_{0} A_{1}}{A_{2} d}\)
Electrostatic Potentials and Capacitance

268110 The cross section of a cable is shown in fig. The inner conductor has a radius of \(10 \mathrm{~mm}\) and the dielectric has a thickness of \(5 \mathrm{~mm}\). The cable is \(8 \mathrm{~km}\) long. Then the capacitance of the cable is \(\left[\log _{e} 1.5=0.4\right]\)

1 \(3.8 \mu \mathrm{F}\)\(\mathrm{F}\)
2 \(1.1 \mu \mathrm{F}\)
3 \(4.8 \times 10^{-10} \mu \mathrm{F}\)
4 \(3.3 \mu \mathrm{F}\)
Electrostatic Potentials and Capacitance

268121 The capacity of a condenser \(\mathrm{A}\) is \(10 \mu \mathrm{F}\) and it is charged to a battery of 100 volt. The battery is disconnected and the condenser A is connected to a condenser B the common potential is \(40 \mathrm{~V}\). The capacity of \(B\) is

1 \(8 \mu \mathrm{F}\)
2 \(15 \mu \mathrm{F}\)
3 \(2 \mu \mathrm{F}\)
4 \(1 \mu F\)
Electrostatic Potentials and Capacitance

268122 A parallel plate capacitor has the space between its plates filled by two slabs of thickness \(\frac{d}{2}\) each and dielectric constant \(K_{1}\) and \(K_{2}\). d is the plate separation of the capacitor. The capacitance of the capacitor is

1 \(\frac{2 \varepsilon_{0} A}{d}\left(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\right)\)
2 \(\frac{2 \varepsilon_{0} A}{d}\left(K_{1}+K_{2}\right)\)
3 \(\frac{2 \varepsilon_{0} A}{d}\left(\frac{K_{1} K_{2}}{K_{1}+K_{2}}\right)\)
4 \(\frac{2 \varepsilon_{0} d}{A}\left(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\right)\)
Electrostatic Potentials and Capacitance

268123 An isolated capacitor of capacitance ' \(C\) ' is charged to a potential ' \(V\) '. Then a dielectric slab of dielectric constant \(\mathrm{K}\) is inserted as shown in fig. The net charge on four surfaces \(1,2,3\) and 4 would be respectively.

1 \(0, C V,-C V, 0\)
2 \(0, \frac{C V}{K}, \frac{-C V}{K}, 0\)
3 \(\mathrm{CV}, 0,0,-\mathrm{CV}\)
4 \(C V, \frac{-C V}{K}, \frac{C V}{K},-C V\)
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Electrostatic Potentials and Capacitance

268109 The area of the positive plate is \(A_{1}\) and the area of the negative plate is \(A_{2}\left(A_{2}\lt A_{1}\right)\). They are parallel to each other and are separated by a distanced. The capacity of a condenser with air as dielectric is

1 \(\frac{\varepsilon_{0} A_{1}}{d}\)
2 \(\frac{\varepsilon_{0} A_{2}}{d}\)
3 \(\frac{\varepsilon_{0} A_{1} A_{2}}{d}\)
4 \(\frac{\varepsilon_{0} A_{1}}{A_{2} d}\)
Electrostatic Potentials and Capacitance

268110 The cross section of a cable is shown in fig. The inner conductor has a radius of \(10 \mathrm{~mm}\) and the dielectric has a thickness of \(5 \mathrm{~mm}\). The cable is \(8 \mathrm{~km}\) long. Then the capacitance of the cable is \(\left[\log _{e} 1.5=0.4\right]\)

1 \(3.8 \mu \mathrm{F}\)\(\mathrm{F}\)
2 \(1.1 \mu \mathrm{F}\)
3 \(4.8 \times 10^{-10} \mu \mathrm{F}\)
4 \(3.3 \mu \mathrm{F}\)
Electrostatic Potentials and Capacitance

268121 The capacity of a condenser \(\mathrm{A}\) is \(10 \mu \mathrm{F}\) and it is charged to a battery of 100 volt. The battery is disconnected and the condenser A is connected to a condenser B the common potential is \(40 \mathrm{~V}\). The capacity of \(B\) is

1 \(8 \mu \mathrm{F}\)
2 \(15 \mu \mathrm{F}\)
3 \(2 \mu \mathrm{F}\)
4 \(1 \mu F\)
Electrostatic Potentials and Capacitance

268122 A parallel plate capacitor has the space between its plates filled by two slabs of thickness \(\frac{d}{2}\) each and dielectric constant \(K_{1}\) and \(K_{2}\). d is the plate separation of the capacitor. The capacitance of the capacitor is

1 \(\frac{2 \varepsilon_{0} A}{d}\left(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\right)\)
2 \(\frac{2 \varepsilon_{0} A}{d}\left(K_{1}+K_{2}\right)\)
3 \(\frac{2 \varepsilon_{0} A}{d}\left(\frac{K_{1} K_{2}}{K_{1}+K_{2}}\right)\)
4 \(\frac{2 \varepsilon_{0} d}{A}\left(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\right)\)
Electrostatic Potentials and Capacitance

268123 An isolated capacitor of capacitance ' \(C\) ' is charged to a potential ' \(V\) '. Then a dielectric slab of dielectric constant \(\mathrm{K}\) is inserted as shown in fig. The net charge on four surfaces \(1,2,3\) and 4 would be respectively.

1 \(0, C V,-C V, 0\)
2 \(0, \frac{C V}{K}, \frac{-C V}{K}, 0\)
3 \(\mathrm{CV}, 0,0,-\mathrm{CV}\)
4 \(C V, \frac{-C V}{K}, \frac{C V}{K},-C V\)
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Electrostatic Potentials and Capacitance

268109 The area of the positive plate is \(A_{1}\) and the area of the negative plate is \(A_{2}\left(A_{2}\lt A_{1}\right)\). They are parallel to each other and are separated by a distanced. The capacity of a condenser with air as dielectric is

1 \(\frac{\varepsilon_{0} A_{1}}{d}\)
2 \(\frac{\varepsilon_{0} A_{2}}{d}\)
3 \(\frac{\varepsilon_{0} A_{1} A_{2}}{d}\)
4 \(\frac{\varepsilon_{0} A_{1}}{A_{2} d}\)
Electrostatic Potentials and Capacitance

268110 The cross section of a cable is shown in fig. The inner conductor has a radius of \(10 \mathrm{~mm}\) and the dielectric has a thickness of \(5 \mathrm{~mm}\). The cable is \(8 \mathrm{~km}\) long. Then the capacitance of the cable is \(\left[\log _{e} 1.5=0.4\right]\)

1 \(3.8 \mu \mathrm{F}\)\(\mathrm{F}\)
2 \(1.1 \mu \mathrm{F}\)
3 \(4.8 \times 10^{-10} \mu \mathrm{F}\)
4 \(3.3 \mu \mathrm{F}\)
Electrostatic Potentials and Capacitance

268121 The capacity of a condenser \(\mathrm{A}\) is \(10 \mu \mathrm{F}\) and it is charged to a battery of 100 volt. The battery is disconnected and the condenser A is connected to a condenser B the common potential is \(40 \mathrm{~V}\). The capacity of \(B\) is

1 \(8 \mu \mathrm{F}\)
2 \(15 \mu \mathrm{F}\)
3 \(2 \mu \mathrm{F}\)
4 \(1 \mu F\)
Electrostatic Potentials and Capacitance

268122 A parallel plate capacitor has the space between its plates filled by two slabs of thickness \(\frac{d}{2}\) each and dielectric constant \(K_{1}\) and \(K_{2}\). d is the plate separation of the capacitor. The capacitance of the capacitor is

1 \(\frac{2 \varepsilon_{0} A}{d}\left(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\right)\)
2 \(\frac{2 \varepsilon_{0} A}{d}\left(K_{1}+K_{2}\right)\)
3 \(\frac{2 \varepsilon_{0} A}{d}\left(\frac{K_{1} K_{2}}{K_{1}+K_{2}}\right)\)
4 \(\frac{2 \varepsilon_{0} d}{A}\left(\frac{K_{1}+K_{2}}{K_{1} K_{2}}\right)\)
Electrostatic Potentials and Capacitance

268123 An isolated capacitor of capacitance ' \(C\) ' is charged to a potential ' \(V\) '. Then a dielectric slab of dielectric constant \(\mathrm{K}\) is inserted as shown in fig. The net charge on four surfaces \(1,2,3\) and 4 would be respectively.

1 \(0, C V,-C V, 0\)
2 \(0, \frac{C V}{K}, \frac{-C V}{K}, 0\)
3 \(\mathrm{CV}, 0,0,-\mathrm{CV}\)
4 \(C V, \frac{-C V}{K}, \frac{C V}{K},-C V\)