CAPACITANCE
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Electrostatic Potentials and Capacitance

268153 Two capacitors \(C_{1}=2 \mu \mathrm{F}\) and \(C_{2}=6 \mu \mathrm{F}\) in series, are connected in parallel to a third capacitor \(C_{3}=4 \mu \mathrm{F}\). Thisarrangement is then connected to a battery of e.m.f. \(=2 \mathrm{~V}\), as shown in figure. The energy lost by the battery in charging the capacitors is

1 \(22 \times 10^{-6} \mathrm{~J}\)
2 \(11 \times 10^{-6} \mathrm{~J}\)
3 \(\left(\frac{32}{3}\right) \times 10^{-6} \mathrm{~J}\)
4 \(\left(\frac{16}{3}\right) \times 10^{-6} \mathrm{~J}\)
Electrostatic Potentials and Capacitance

268158 The equivalent capacity between the points\(A\) and \(B\) in theadjoining circuit will be

1 \(\mathrm{C}\)
2 \(2 C\)
3 \(3 C\)
4 4
Electrostatic Potentials and Capacitance

268161 In the adjoining diagram, the condenser\(C\) will be fully charged to potential \(V\) if

1 \(S_{1}\) and \(S_{2}\) both areopen
2 \(S_{1}^{1}\) and \(S_{2}^{2}\) both are closed
3 \(S_{1}^{1}\) is closed and \(S_{2}\) is open
4 \(S_{1}^{1}\) is open and \(S_{2}\) is closed.
Electrostatic Potentials and Capacitance

268163 The capacitance\(C_{A B}\) in the given network

1 \(7 \mu F\)
2 \(\frac{50}{7} \mu F\)
3 \(7.5 \mu \mathrm{F}\) \(5 \mu\)
4 \(\frac{7}{50} \mu F\)
Electrostatic Potentials and Capacitance

268168 O ne plate of a capacitor is connected to a spring as shown in figure. Area of both the plates is A. In steady state; separation between the plates is \(0.8 \mathrm{~d}\) (spring was unstretched and the distance between the plates was d, when the capacitor was uncharged). The force constant of the spring is approximately

1 \(\frac{4 \epsilon_{0} A E^{2}}{d^{3}}\)
2 \(\frac{2 \epsilon_{0}}{d^{2}}\)
3 \(\frac{6 \epsilon_{0} E^{2}}{A d^{3}}\)
4 \(\frac{\epsilon_{0} A E^{3}}{2 d^{3}}\)
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Electrostatic Potentials and Capacitance

268153 Two capacitors \(C_{1}=2 \mu \mathrm{F}\) and \(C_{2}=6 \mu \mathrm{F}\) in series, are connected in parallel to a third capacitor \(C_{3}=4 \mu \mathrm{F}\). Thisarrangement is then connected to a battery of e.m.f. \(=2 \mathrm{~V}\), as shown in figure. The energy lost by the battery in charging the capacitors is

1 \(22 \times 10^{-6} \mathrm{~J}\)
2 \(11 \times 10^{-6} \mathrm{~J}\)
3 \(\left(\frac{32}{3}\right) \times 10^{-6} \mathrm{~J}\)
4 \(\left(\frac{16}{3}\right) \times 10^{-6} \mathrm{~J}\)
Electrostatic Potentials and Capacitance

268158 The equivalent capacity between the points\(A\) and \(B\) in theadjoining circuit will be

1 \(\mathrm{C}\)
2 \(2 C\)
3 \(3 C\)
4 4
Electrostatic Potentials and Capacitance

268161 In the adjoining diagram, the condenser\(C\) will be fully charged to potential \(V\) if

1 \(S_{1}\) and \(S_{2}\) both areopen
2 \(S_{1}^{1}\) and \(S_{2}^{2}\) both are closed
3 \(S_{1}^{1}\) is closed and \(S_{2}\) is open
4 \(S_{1}^{1}\) is open and \(S_{2}\) is closed.
Electrostatic Potentials and Capacitance

268163 The capacitance\(C_{A B}\) in the given network

1 \(7 \mu F\)
2 \(\frac{50}{7} \mu F\)
3 \(7.5 \mu \mathrm{F}\) \(5 \mu\)
4 \(\frac{7}{50} \mu F\)
Electrostatic Potentials and Capacitance

268168 O ne plate of a capacitor is connected to a spring as shown in figure. Area of both the plates is A. In steady state; separation between the plates is \(0.8 \mathrm{~d}\) (spring was unstretched and the distance between the plates was d, when the capacitor was uncharged). The force constant of the spring is approximately

1 \(\frac{4 \epsilon_{0} A E^{2}}{d^{3}}\)
2 \(\frac{2 \epsilon_{0}}{d^{2}}\)
3 \(\frac{6 \epsilon_{0} E^{2}}{A d^{3}}\)
4 \(\frac{\epsilon_{0} A E^{3}}{2 d^{3}}\)
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Electrostatic Potentials and Capacitance

268153 Two capacitors \(C_{1}=2 \mu \mathrm{F}\) and \(C_{2}=6 \mu \mathrm{F}\) in series, are connected in parallel to a third capacitor \(C_{3}=4 \mu \mathrm{F}\). Thisarrangement is then connected to a battery of e.m.f. \(=2 \mathrm{~V}\), as shown in figure. The energy lost by the battery in charging the capacitors is

1 \(22 \times 10^{-6} \mathrm{~J}\)
2 \(11 \times 10^{-6} \mathrm{~J}\)
3 \(\left(\frac{32}{3}\right) \times 10^{-6} \mathrm{~J}\)
4 \(\left(\frac{16}{3}\right) \times 10^{-6} \mathrm{~J}\)
Electrostatic Potentials and Capacitance

268158 The equivalent capacity between the points\(A\) and \(B\) in theadjoining circuit will be

1 \(\mathrm{C}\)
2 \(2 C\)
3 \(3 C\)
4 4
Electrostatic Potentials and Capacitance

268161 In the adjoining diagram, the condenser\(C\) will be fully charged to potential \(V\) if

1 \(S_{1}\) and \(S_{2}\) both areopen
2 \(S_{1}^{1}\) and \(S_{2}^{2}\) both are closed
3 \(S_{1}^{1}\) is closed and \(S_{2}\) is open
4 \(S_{1}^{1}\) is open and \(S_{2}\) is closed.
Electrostatic Potentials and Capacitance

268163 The capacitance\(C_{A B}\) in the given network

1 \(7 \mu F\)
2 \(\frac{50}{7} \mu F\)
3 \(7.5 \mu \mathrm{F}\) \(5 \mu\)
4 \(\frac{7}{50} \mu F\)
Electrostatic Potentials and Capacitance

268168 O ne plate of a capacitor is connected to a spring as shown in figure. Area of both the plates is A. In steady state; separation between the plates is \(0.8 \mathrm{~d}\) (spring was unstretched and the distance between the plates was d, when the capacitor was uncharged). The force constant of the spring is approximately

1 \(\frac{4 \epsilon_{0} A E^{2}}{d^{3}}\)
2 \(\frac{2 \epsilon_{0}}{d^{2}}\)
3 \(\frac{6 \epsilon_{0} E^{2}}{A d^{3}}\)
4 \(\frac{\epsilon_{0} A E^{3}}{2 d^{3}}\)
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Electrostatic Potentials and Capacitance

268153 Two capacitors \(C_{1}=2 \mu \mathrm{F}\) and \(C_{2}=6 \mu \mathrm{F}\) in series, are connected in parallel to a third capacitor \(C_{3}=4 \mu \mathrm{F}\). Thisarrangement is then connected to a battery of e.m.f. \(=2 \mathrm{~V}\), as shown in figure. The energy lost by the battery in charging the capacitors is

1 \(22 \times 10^{-6} \mathrm{~J}\)
2 \(11 \times 10^{-6} \mathrm{~J}\)
3 \(\left(\frac{32}{3}\right) \times 10^{-6} \mathrm{~J}\)
4 \(\left(\frac{16}{3}\right) \times 10^{-6} \mathrm{~J}\)
Electrostatic Potentials and Capacitance

268158 The equivalent capacity between the points\(A\) and \(B\) in theadjoining circuit will be

1 \(\mathrm{C}\)
2 \(2 C\)
3 \(3 C\)
4 4
Electrostatic Potentials and Capacitance

268161 In the adjoining diagram, the condenser\(C\) will be fully charged to potential \(V\) if

1 \(S_{1}\) and \(S_{2}\) both areopen
2 \(S_{1}^{1}\) and \(S_{2}^{2}\) both are closed
3 \(S_{1}^{1}\) is closed and \(S_{2}\) is open
4 \(S_{1}^{1}\) is open and \(S_{2}\) is closed.
Electrostatic Potentials and Capacitance

268163 The capacitance\(C_{A B}\) in the given network

1 \(7 \mu F\)
2 \(\frac{50}{7} \mu F\)
3 \(7.5 \mu \mathrm{F}\) \(5 \mu\)
4 \(\frac{7}{50} \mu F\)
Electrostatic Potentials and Capacitance

268168 O ne plate of a capacitor is connected to a spring as shown in figure. Area of both the plates is A. In steady state; separation between the plates is \(0.8 \mathrm{~d}\) (spring was unstretched and the distance between the plates was d, when the capacitor was uncharged). The force constant of the spring is approximately

1 \(\frac{4 \epsilon_{0} A E^{2}}{d^{3}}\)
2 \(\frac{2 \epsilon_{0}}{d^{2}}\)
3 \(\frac{6 \epsilon_{0} E^{2}}{A d^{3}}\)
4 \(\frac{\epsilon_{0} A E^{3}}{2 d^{3}}\)
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Electrostatic Potentials and Capacitance

268153 Two capacitors \(C_{1}=2 \mu \mathrm{F}\) and \(C_{2}=6 \mu \mathrm{F}\) in series, are connected in parallel to a third capacitor \(C_{3}=4 \mu \mathrm{F}\). Thisarrangement is then connected to a battery of e.m.f. \(=2 \mathrm{~V}\), as shown in figure. The energy lost by the battery in charging the capacitors is

1 \(22 \times 10^{-6} \mathrm{~J}\)
2 \(11 \times 10^{-6} \mathrm{~J}\)
3 \(\left(\frac{32}{3}\right) \times 10^{-6} \mathrm{~J}\)
4 \(\left(\frac{16}{3}\right) \times 10^{-6} \mathrm{~J}\)
Electrostatic Potentials and Capacitance

268158 The equivalent capacity between the points\(A\) and \(B\) in theadjoining circuit will be

1 \(\mathrm{C}\)
2 \(2 C\)
3 \(3 C\)
4 4
Electrostatic Potentials and Capacitance

268161 In the adjoining diagram, the condenser\(C\) will be fully charged to potential \(V\) if

1 \(S_{1}\) and \(S_{2}\) both areopen
2 \(S_{1}^{1}\) and \(S_{2}^{2}\) both are closed
3 \(S_{1}^{1}\) is closed and \(S_{2}\) is open
4 \(S_{1}^{1}\) is open and \(S_{2}\) is closed.
Electrostatic Potentials and Capacitance

268163 The capacitance\(C_{A B}\) in the given network

1 \(7 \mu F\)
2 \(\frac{50}{7} \mu F\)
3 \(7.5 \mu \mathrm{F}\) \(5 \mu\)
4 \(\frac{7}{50} \mu F\)
Electrostatic Potentials and Capacitance

268168 O ne plate of a capacitor is connected to a spring as shown in figure. Area of both the plates is A. In steady state; separation between the plates is \(0.8 \mathrm{~d}\) (spring was unstretched and the distance between the plates was d, when the capacitor was uncharged). The force constant of the spring is approximately

1 \(\frac{4 \epsilon_{0} A E^{2}}{d^{3}}\)
2 \(\frac{2 \epsilon_{0}}{d^{2}}\)
3 \(\frac{6 \epsilon_{0} E^{2}}{A d^{3}}\)
4 \(\frac{\epsilon_{0} A E^{3}}{2 d^{3}}\)