CAPACITORSIN SERIES AND IN PARALLEL
Electrostatic Potentials and Capacitance

268124 A parallel plate capacitor with plate area ' \(\mathrm{A}\) ' and separation ' \(\mathrm{d}\) ' is filled with two dielectrics of dielectric constants \(K_{1}\) and \(K_{2}\). If the permittivity of free space is \(\epsilon_{0}\), the capacitance of the capacitor is given by

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

268081 When two capacitors are joined in series theresultancecapacity is \(2.4 \mu \mathrm{F}\) and when thesame two arejoined in parallel the resultant capacity is \(10 \mu \mathrm{F}\). Their individual capacitiesare

1 \(7 \mu F, 3 \mu F\)
2 \(1 \mu F, 9 \mu F\)
3 \(6 \mu F, 4 \mu F\)
4 \(48 \mu F, 2 \mu F\)
Electrostatic Potentials and Capacitance

268082 Three condensers\(1 \mu F, 2 \mu F\) and \(3 \mu F\) are connected in series to a p.d. of 330 volt. The p.d across the plates of \(3 \mu \mathrm{F}\) is

1 \(180 \mathrm{~V}\)
2 \(300 \mathrm{~V}\)
3 \(60 \mathrm{~V}\)
4 \(270 \mathrm{~V}\)
Electrostatic Potentials and Capacitance

268087 Three capacitors of\(3 \mu F, 2 \mu F\) and \(6 \mu F\) are connected in series. W hen a battery of \(10 \mathrm{~V}\) is connected to this combination then charge on \(3 \mu F\) capacitor will be

1 \(5 \mu C\)
2 \(10 \mu \mathrm{C}\)
3 \(15 \mu C\)
4 \(20 \mu \mathrm{C}\)
Electrostatic Potentials and Capacitance

268095 The ratio of the resultant capacities when three capacitors of \(2 \mu \mathrm{F}, 4 \mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) are connected first in series and then in parallel is

1 \(1: 11\)
2 \(11: 1\)
3 \(12: 1\)
4 \(1: 12\)
Electrostatic Potentials and Capacitance

268124 A parallel plate capacitor with plate area ' \(\mathrm{A}\) ' and separation ' \(\mathrm{d}\) ' is filled with two dielectrics of dielectric constants \(K_{1}\) and \(K_{2}\). If the permittivity of free space is \(\epsilon_{0}\), the capacitance of the capacitor is given by

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

268081 When two capacitors are joined in series theresultancecapacity is \(2.4 \mu \mathrm{F}\) and when thesame two arejoined in parallel the resultant capacity is \(10 \mu \mathrm{F}\). Their individual capacitiesare

1 \(7 \mu F, 3 \mu F\)
2 \(1 \mu F, 9 \mu F\)
3 \(6 \mu F, 4 \mu F\)
4 \(48 \mu F, 2 \mu F\)
Electrostatic Potentials and Capacitance

268082 Three condensers\(1 \mu F, 2 \mu F\) and \(3 \mu F\) are connected in series to a p.d. of 330 volt. The p.d across the plates of \(3 \mu \mathrm{F}\) is

1 \(180 \mathrm{~V}\)
2 \(300 \mathrm{~V}\)
3 \(60 \mathrm{~V}\)
4 \(270 \mathrm{~V}\)
Electrostatic Potentials and Capacitance

268087 Three capacitors of\(3 \mu F, 2 \mu F\) and \(6 \mu F\) are connected in series. W hen a battery of \(10 \mathrm{~V}\) is connected to this combination then charge on \(3 \mu F\) capacitor will be

1 \(5 \mu C\)
2 \(10 \mu \mathrm{C}\)
3 \(15 \mu C\)
4 \(20 \mu \mathrm{C}\)
Electrostatic Potentials and Capacitance

268095 The ratio of the resultant capacities when three capacitors of \(2 \mu \mathrm{F}, 4 \mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) are connected first in series and then in parallel is

1 \(1: 11\)
2 \(11: 1\)
3 \(12: 1\)
4 \(1: 12\)
Electrostatic Potentials and Capacitance

268124 A parallel plate capacitor with plate area ' \(\mathrm{A}\) ' and separation ' \(\mathrm{d}\) ' is filled with two dielectrics of dielectric constants \(K_{1}\) and \(K_{2}\). If the permittivity of free space is \(\epsilon_{0}\), the capacitance of the capacitor is given by

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

268081 When two capacitors are joined in series theresultancecapacity is \(2.4 \mu \mathrm{F}\) and when thesame two arejoined in parallel the resultant capacity is \(10 \mu \mathrm{F}\). Their individual capacitiesare

1 \(7 \mu F, 3 \mu F\)
2 \(1 \mu F, 9 \mu F\)
3 \(6 \mu F, 4 \mu F\)
4 \(48 \mu F, 2 \mu F\)
Electrostatic Potentials and Capacitance

268082 Three condensers\(1 \mu F, 2 \mu F\) and \(3 \mu F\) are connected in series to a p.d. of 330 volt. The p.d across the plates of \(3 \mu \mathrm{F}\) is

1 \(180 \mathrm{~V}\)
2 \(300 \mathrm{~V}\)
3 \(60 \mathrm{~V}\)
4 \(270 \mathrm{~V}\)
Electrostatic Potentials and Capacitance

268087 Three capacitors of\(3 \mu F, 2 \mu F\) and \(6 \mu F\) are connected in series. W hen a battery of \(10 \mathrm{~V}\) is connected to this combination then charge on \(3 \mu F\) capacitor will be

1 \(5 \mu C\)
2 \(10 \mu \mathrm{C}\)
3 \(15 \mu C\)
4 \(20 \mu \mathrm{C}\)
Electrostatic Potentials and Capacitance

268095 The ratio of the resultant capacities when three capacitors of \(2 \mu \mathrm{F}, 4 \mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) are connected first in series and then in parallel is

1 \(1: 11\)
2 \(11: 1\)
3 \(12: 1\)
4 \(1: 12\)
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Electrostatic Potentials and Capacitance

268124 A parallel plate capacitor with plate area ' \(\mathrm{A}\) ' and separation ' \(\mathrm{d}\) ' is filled with two dielectrics of dielectric constants \(K_{1}\) and \(K_{2}\). If the permittivity of free space is \(\epsilon_{0}\), the capacitance of the capacitor is given by

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

268081 When two capacitors are joined in series theresultancecapacity is \(2.4 \mu \mathrm{F}\) and when thesame two arejoined in parallel the resultant capacity is \(10 \mu \mathrm{F}\). Their individual capacitiesare

1 \(7 \mu F, 3 \mu F\)
2 \(1 \mu F, 9 \mu F\)
3 \(6 \mu F, 4 \mu F\)
4 \(48 \mu F, 2 \mu F\)
Electrostatic Potentials and Capacitance

268082 Three condensers\(1 \mu F, 2 \mu F\) and \(3 \mu F\) are connected in series to a p.d. of 330 volt. The p.d across the plates of \(3 \mu \mathrm{F}\) is

1 \(180 \mathrm{~V}\)
2 \(300 \mathrm{~V}\)
3 \(60 \mathrm{~V}\)
4 \(270 \mathrm{~V}\)
Electrostatic Potentials and Capacitance

268087 Three capacitors of\(3 \mu F, 2 \mu F\) and \(6 \mu F\) are connected in series. W hen a battery of \(10 \mathrm{~V}\) is connected to this combination then charge on \(3 \mu F\) capacitor will be

1 \(5 \mu C\)
2 \(10 \mu \mathrm{C}\)
3 \(15 \mu C\)
4 \(20 \mu \mathrm{C}\)
Electrostatic Potentials and Capacitance

268095 The ratio of the resultant capacities when three capacitors of \(2 \mu \mathrm{F}, 4 \mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) are connected first in series and then in parallel is

1 \(1: 11\)
2 \(11: 1\)
3 \(12: 1\)
4 \(1: 12\)
Electrostatic Potentials and Capacitance

268124 A parallel plate capacitor with plate area ' \(\mathrm{A}\) ' and separation ' \(\mathrm{d}\) ' is filled with two dielectrics of dielectric constants \(K_{1}\) and \(K_{2}\). If the permittivity of free space is \(\epsilon_{0}\), the capacitance of the capacitor is given by

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

268081 When two capacitors are joined in series theresultancecapacity is \(2.4 \mu \mathrm{F}\) and when thesame two arejoined in parallel the resultant capacity is \(10 \mu \mathrm{F}\). Their individual capacitiesare

1 \(7 \mu F, 3 \mu F\)
2 \(1 \mu F, 9 \mu F\)
3 \(6 \mu F, 4 \mu F\)
4 \(48 \mu F, 2 \mu F\)
Electrostatic Potentials and Capacitance

268082 Three condensers\(1 \mu F, 2 \mu F\) and \(3 \mu F\) are connected in series to a p.d. of 330 volt. The p.d across the plates of \(3 \mu \mathrm{F}\) is

1 \(180 \mathrm{~V}\)
2 \(300 \mathrm{~V}\)
3 \(60 \mathrm{~V}\)
4 \(270 \mathrm{~V}\)
Electrostatic Potentials and Capacitance

268087 Three capacitors of\(3 \mu F, 2 \mu F\) and \(6 \mu F\) are connected in series. W hen a battery of \(10 \mathrm{~V}\) is connected to this combination then charge on \(3 \mu F\) capacitor will be

1 \(5 \mu C\)
2 \(10 \mu \mathrm{C}\)
3 \(15 \mu C\)
4 \(20 \mu \mathrm{C}\)
Electrostatic Potentials and Capacitance

268095 The ratio of the resultant capacities when three capacitors of \(2 \mu \mathrm{F}, 4 \mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) are connected first in series and then in parallel is

1 \(1: 11\)
2 \(11: 1\)
3 \(12: 1\)
4 \(1: 12\)