ENERGY STORED IN A CONDENSER AND TYPES OF CAPACITORS
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Electrostatic Potentials and Capacitance

268049 Three identical condensersare connected together in four different ways. First all of them are connected in series and the equivalent capacity is \(\mathrm{C}_{1}\). Next all of them are connected in parallel and the equivalent capacity is \(\mathrm{C}_{2^{2}}\). Next two of them are connected in series and the third one connected in parallel to the combination and the equivalent capacity is \(\mathrm{C}_{3}\). Next two of them are connected in parallel and the third
one connected in series with the combination and the equivalent capacity is \(\mathrm{C}_{4}\). Which of the following is correct ascending order of the equivalent capacities?

1 \(C_{1}\lt C_{3}\lt C_{4}\lt C_{2}\)
2 \(C_{1}\lt C_{4}\lt C_{3}\lt C_{2}\)
3 \(C_{2}\lt C_{3}\lt C_{4}\lt C_{1}\)
4 \(C_{2}\lt C_{4}\lt C_{3}\lt C_{1}\)
Electrostatic Potentials and Capacitance

268038 Figure shows two capacitors connected in series and joined to a cell. The graph shows the variation in potential as one moves from left to right on the branch containing capacitors.

1 \(C_{1}>C_{2}\)
2 \(C_{1}=C_{2}\)
3 \(C_{1}\lt C_{2}\)
4 data insufficient to conclude the answer
Electrostatic Potentials and Capacitance

268050 On a capacitor of capacitance\(C_{0}\) following steps are performed in the order as given in column I.
(A) Capacitor is charged by connecting it across a battery of emf \(E_{0}\)
(B) Dielectric of dielectric constant \(K\) and thickness d is inserted
(C) C apacitor is disconnected from battery
(D) Separation between plates is doubled

|Column-I (Steps performed) |Column-II (Final value of Q uantity (Symbols have usual meaning) (Steps performed)|
|-----|------|
|(a) \((A)(D)(C)(B)\)|(p) \(Q=\frac{C_{0} E_{0}}{2}\)|
|(b) (D)(A)(C)(B)|(q) \(Q=\frac{K C_{0} E_{0}}{K+1}\)|
|(c) \((B)(A)(C)(D)\)|(r) \(C=\frac{K C_{0}}{K+1}\)|
|(d) \((A)(B)(D)(C)\)|(s) \(V=\frac{E_{0}(K+1)}{2 K}\)|

1 \(a-p, r, s, b-p, r, s, c-r, d-q, r\)
2 \(a-p, b-p,r c-r, d-q,\)
3 \(a-p,s, b-r,s, c-r, d-q,\)
4 \(a-r, s, b-s, c-r, d-q, r\)
Electrostatic Potentials and Capacitance

268051 In the circuit, both capacitors areindentical. C olumn I indicates action done on capacitors 1 and Column II indicates effect on capacitor 2

1 \(ar, b-p,q, c-s, d-p,q\)
2 \(arr, b-p, c-s, d-q\)
3 \(a-r, b-p, c-r, d-q\)
4 \(a-s, b-q, c-s, d-q\)
Electrostatic Potentials and Capacitance

268052 The potential across a\(3 \mu \mathrm{F}\) capacitor is \(12 \mathrm{~V}\) when it is not connected to anything. It is then connected in parallel with an uncharged \(6 \mu \mathrm{F}\) capacitor. At equilibrium, the charge and potential difference across the capacitor 3 \(\mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) arelisted in column I. M atch it with column III.
|Column-I|Column-II|
|------|------|
|(a) charge on \(3 \mu \mathrm{F}\) capacitor|(p) \(12 \mu \mathrm{C}\)|
|(b) charge on \(6 \mu \mathrm{F}\) capacitor|(q) \(24 \mu \mathrm{F}\)|
|(c) potential difference across \(3 \mu \mathrm{F}\) |(r) \(8 \mathrm{~V}\) capacitor|
|(d) potential difference across \(6 \mu \mathrm{F}\) |(s) \(4 \mathrm{~V}\) capacitor|

1 ar, b-p, c-s, d-q
2 a-p, b-q, c-s, d-s
3 ar, b-p, c-q, d-q
4 arr, b-q, c-s, d-q
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Electrostatic Potentials and Capacitance

268049 Three identical condensersare connected together in four different ways. First all of them are connected in series and the equivalent capacity is \(\mathrm{C}_{1}\). Next all of them are connected in parallel and the equivalent capacity is \(\mathrm{C}_{2^{2}}\). Next two of them are connected in series and the third one connected in parallel to the combination and the equivalent capacity is \(\mathrm{C}_{3}\). Next two of them are connected in parallel and the third
one connected in series with the combination and the equivalent capacity is \(\mathrm{C}_{4}\). Which of the following is correct ascending order of the equivalent capacities?

1 \(C_{1}\lt C_{3}\lt C_{4}\lt C_{2}\)
2 \(C_{1}\lt C_{4}\lt C_{3}\lt C_{2}\)
3 \(C_{2}\lt C_{3}\lt C_{4}\lt C_{1}\)
4 \(C_{2}\lt C_{4}\lt C_{3}\lt C_{1}\)
Electrostatic Potentials and Capacitance

268038 Figure shows two capacitors connected in series and joined to a cell. The graph shows the variation in potential as one moves from left to right on the branch containing capacitors.

1 \(C_{1}>C_{2}\)
2 \(C_{1}=C_{2}\)
3 \(C_{1}\lt C_{2}\)
4 data insufficient to conclude the answer
Electrostatic Potentials and Capacitance

268050 On a capacitor of capacitance\(C_{0}\) following steps are performed in the order as given in column I.
(A) Capacitor is charged by connecting it across a battery of emf \(E_{0}\)
(B) Dielectric of dielectric constant \(K\) and thickness d is inserted
(C) C apacitor is disconnected from battery
(D) Separation between plates is doubled

|Column-I (Steps performed) |Column-II (Final value of Q uantity (Symbols have usual meaning) (Steps performed)|
|-----|------|
|(a) \((A)(D)(C)(B)\)|(p) \(Q=\frac{C_{0} E_{0}}{2}\)|
|(b) (D)(A)(C)(B)|(q) \(Q=\frac{K C_{0} E_{0}}{K+1}\)|
|(c) \((B)(A)(C)(D)\)|(r) \(C=\frac{K C_{0}}{K+1}\)|
|(d) \((A)(B)(D)(C)\)|(s) \(V=\frac{E_{0}(K+1)}{2 K}\)|

1 \(a-p, r, s, b-p, r, s, c-r, d-q, r\)
2 \(a-p, b-p,r c-r, d-q,\)
3 \(a-p,s, b-r,s, c-r, d-q,\)
4 \(a-r, s, b-s, c-r, d-q, r\)
Electrostatic Potentials and Capacitance

268051 In the circuit, both capacitors areindentical. C olumn I indicates action done on capacitors 1 and Column II indicates effect on capacitor 2

1 \(ar, b-p,q, c-s, d-p,q\)
2 \(arr, b-p, c-s, d-q\)
3 \(a-r, b-p, c-r, d-q\)
4 \(a-s, b-q, c-s, d-q\)
Electrostatic Potentials and Capacitance

268052 The potential across a\(3 \mu \mathrm{F}\) capacitor is \(12 \mathrm{~V}\) when it is not connected to anything. It is then connected in parallel with an uncharged \(6 \mu \mathrm{F}\) capacitor. At equilibrium, the charge and potential difference across the capacitor 3 \(\mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) arelisted in column I. M atch it with column III.
|Column-I|Column-II|
|------|------|
|(a) charge on \(3 \mu \mathrm{F}\) capacitor|(p) \(12 \mu \mathrm{C}\)|
|(b) charge on \(6 \mu \mathrm{F}\) capacitor|(q) \(24 \mu \mathrm{F}\)|
|(c) potential difference across \(3 \mu \mathrm{F}\) |(r) \(8 \mathrm{~V}\) capacitor|
|(d) potential difference across \(6 \mu \mathrm{F}\) |(s) \(4 \mathrm{~V}\) capacitor|

1 ar, b-p, c-s, d-q
2 a-p, b-q, c-s, d-s
3 ar, b-p, c-q, d-q
4 arr, b-q, c-s, d-q
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Electrostatic Potentials and Capacitance

268049 Three identical condensersare connected together in four different ways. First all of them are connected in series and the equivalent capacity is \(\mathrm{C}_{1}\). Next all of them are connected in parallel and the equivalent capacity is \(\mathrm{C}_{2^{2}}\). Next two of them are connected in series and the third one connected in parallel to the combination and the equivalent capacity is \(\mathrm{C}_{3}\). Next two of them are connected in parallel and the third
one connected in series with the combination and the equivalent capacity is \(\mathrm{C}_{4}\). Which of the following is correct ascending order of the equivalent capacities?

1 \(C_{1}\lt C_{3}\lt C_{4}\lt C_{2}\)
2 \(C_{1}\lt C_{4}\lt C_{3}\lt C_{2}\)
3 \(C_{2}\lt C_{3}\lt C_{4}\lt C_{1}\)
4 \(C_{2}\lt C_{4}\lt C_{3}\lt C_{1}\)
Electrostatic Potentials and Capacitance

268038 Figure shows two capacitors connected in series and joined to a cell. The graph shows the variation in potential as one moves from left to right on the branch containing capacitors.

1 \(C_{1}>C_{2}\)
2 \(C_{1}=C_{2}\)
3 \(C_{1}\lt C_{2}\)
4 data insufficient to conclude the answer
Electrostatic Potentials and Capacitance

268050 On a capacitor of capacitance\(C_{0}\) following steps are performed in the order as given in column I.
(A) Capacitor is charged by connecting it across a battery of emf \(E_{0}\)
(B) Dielectric of dielectric constant \(K\) and thickness d is inserted
(C) C apacitor is disconnected from battery
(D) Separation between plates is doubled

|Column-I (Steps performed) |Column-II (Final value of Q uantity (Symbols have usual meaning) (Steps performed)|
|-----|------|
|(a) \((A)(D)(C)(B)\)|(p) \(Q=\frac{C_{0} E_{0}}{2}\)|
|(b) (D)(A)(C)(B)|(q) \(Q=\frac{K C_{0} E_{0}}{K+1}\)|
|(c) \((B)(A)(C)(D)\)|(r) \(C=\frac{K C_{0}}{K+1}\)|
|(d) \((A)(B)(D)(C)\)|(s) \(V=\frac{E_{0}(K+1)}{2 K}\)|

1 \(a-p, r, s, b-p, r, s, c-r, d-q, r\)
2 \(a-p, b-p,r c-r, d-q,\)
3 \(a-p,s, b-r,s, c-r, d-q,\)
4 \(a-r, s, b-s, c-r, d-q, r\)
Electrostatic Potentials and Capacitance

268051 In the circuit, both capacitors areindentical. C olumn I indicates action done on capacitors 1 and Column II indicates effect on capacitor 2

1 \(ar, b-p,q, c-s, d-p,q\)
2 \(arr, b-p, c-s, d-q\)
3 \(a-r, b-p, c-r, d-q\)
4 \(a-s, b-q, c-s, d-q\)
Electrostatic Potentials and Capacitance

268052 The potential across a\(3 \mu \mathrm{F}\) capacitor is \(12 \mathrm{~V}\) when it is not connected to anything. It is then connected in parallel with an uncharged \(6 \mu \mathrm{F}\) capacitor. At equilibrium, the charge and potential difference across the capacitor 3 \(\mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) arelisted in column I. M atch it with column III.
|Column-I|Column-II|
|------|------|
|(a) charge on \(3 \mu \mathrm{F}\) capacitor|(p) \(12 \mu \mathrm{C}\)|
|(b) charge on \(6 \mu \mathrm{F}\) capacitor|(q) \(24 \mu \mathrm{F}\)|
|(c) potential difference across \(3 \mu \mathrm{F}\) |(r) \(8 \mathrm{~V}\) capacitor|
|(d) potential difference across \(6 \mu \mathrm{F}\) |(s) \(4 \mathrm{~V}\) capacitor|

1 ar, b-p, c-s, d-q
2 a-p, b-q, c-s, d-s
3 ar, b-p, c-q, d-q
4 arr, b-q, c-s, d-q
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Electrostatic Potentials and Capacitance

268049 Three identical condensersare connected together in four different ways. First all of them are connected in series and the equivalent capacity is \(\mathrm{C}_{1}\). Next all of them are connected in parallel and the equivalent capacity is \(\mathrm{C}_{2^{2}}\). Next two of them are connected in series and the third one connected in parallel to the combination and the equivalent capacity is \(\mathrm{C}_{3}\). Next two of them are connected in parallel and the third
one connected in series with the combination and the equivalent capacity is \(\mathrm{C}_{4}\). Which of the following is correct ascending order of the equivalent capacities?

1 \(C_{1}\lt C_{3}\lt C_{4}\lt C_{2}\)
2 \(C_{1}\lt C_{4}\lt C_{3}\lt C_{2}\)
3 \(C_{2}\lt C_{3}\lt C_{4}\lt C_{1}\)
4 \(C_{2}\lt C_{4}\lt C_{3}\lt C_{1}\)
Electrostatic Potentials and Capacitance

268038 Figure shows two capacitors connected in series and joined to a cell. The graph shows the variation in potential as one moves from left to right on the branch containing capacitors.

1 \(C_{1}>C_{2}\)
2 \(C_{1}=C_{2}\)
3 \(C_{1}\lt C_{2}\)
4 data insufficient to conclude the answer
Electrostatic Potentials and Capacitance

268050 On a capacitor of capacitance\(C_{0}\) following steps are performed in the order as given in column I.
(A) Capacitor is charged by connecting it across a battery of emf \(E_{0}\)
(B) Dielectric of dielectric constant \(K\) and thickness d is inserted
(C) C apacitor is disconnected from battery
(D) Separation between plates is doubled

|Column-I (Steps performed) |Column-II (Final value of Q uantity (Symbols have usual meaning) (Steps performed)|
|-----|------|
|(a) \((A)(D)(C)(B)\)|(p) \(Q=\frac{C_{0} E_{0}}{2}\)|
|(b) (D)(A)(C)(B)|(q) \(Q=\frac{K C_{0} E_{0}}{K+1}\)|
|(c) \((B)(A)(C)(D)\)|(r) \(C=\frac{K C_{0}}{K+1}\)|
|(d) \((A)(B)(D)(C)\)|(s) \(V=\frac{E_{0}(K+1)}{2 K}\)|

1 \(a-p, r, s, b-p, r, s, c-r, d-q, r\)
2 \(a-p, b-p,r c-r, d-q,\)
3 \(a-p,s, b-r,s, c-r, d-q,\)
4 \(a-r, s, b-s, c-r, d-q, r\)
Electrostatic Potentials and Capacitance

268051 In the circuit, both capacitors areindentical. C olumn I indicates action done on capacitors 1 and Column II indicates effect on capacitor 2

1 \(ar, b-p,q, c-s, d-p,q\)
2 \(arr, b-p, c-s, d-q\)
3 \(a-r, b-p, c-r, d-q\)
4 \(a-s, b-q, c-s, d-q\)
Electrostatic Potentials and Capacitance

268052 The potential across a\(3 \mu \mathrm{F}\) capacitor is \(12 \mathrm{~V}\) when it is not connected to anything. It is then connected in parallel with an uncharged \(6 \mu \mathrm{F}\) capacitor. At equilibrium, the charge and potential difference across the capacitor 3 \(\mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) arelisted in column I. M atch it with column III.
|Column-I|Column-II|
|------|------|
|(a) charge on \(3 \mu \mathrm{F}\) capacitor|(p) \(12 \mu \mathrm{C}\)|
|(b) charge on \(6 \mu \mathrm{F}\) capacitor|(q) \(24 \mu \mathrm{F}\)|
|(c) potential difference across \(3 \mu \mathrm{F}\) |(r) \(8 \mathrm{~V}\) capacitor|
|(d) potential difference across \(6 \mu \mathrm{F}\) |(s) \(4 \mathrm{~V}\) capacitor|

1 ar, b-p, c-s, d-q
2 a-p, b-q, c-s, d-s
3 ar, b-p, c-q, d-q
4 arr, b-q, c-s, d-q
NEET DIGITAL LIBRARY
Electrostatic Potentials and Capacitance

268049 Three identical condensersare connected together in four different ways. First all of them are connected in series and the equivalent capacity is \(\mathrm{C}_{1}\). Next all of them are connected in parallel and the equivalent capacity is \(\mathrm{C}_{2^{2}}\). Next two of them are connected in series and the third one connected in parallel to the combination and the equivalent capacity is \(\mathrm{C}_{3}\). Next two of them are connected in parallel and the third
one connected in series with the combination and the equivalent capacity is \(\mathrm{C}_{4}\). Which of the following is correct ascending order of the equivalent capacities?

1 \(C_{1}\lt C_{3}\lt C_{4}\lt C_{2}\)
2 \(C_{1}\lt C_{4}\lt C_{3}\lt C_{2}\)
3 \(C_{2}\lt C_{3}\lt C_{4}\lt C_{1}\)
4 \(C_{2}\lt C_{4}\lt C_{3}\lt C_{1}\)
Electrostatic Potentials and Capacitance

268038 Figure shows two capacitors connected in series and joined to a cell. The graph shows the variation in potential as one moves from left to right on the branch containing capacitors.

1 \(C_{1}>C_{2}\)
2 \(C_{1}=C_{2}\)
3 \(C_{1}\lt C_{2}\)
4 data insufficient to conclude the answer
Electrostatic Potentials and Capacitance

268050 On a capacitor of capacitance\(C_{0}\) following steps are performed in the order as given in column I.
(A) Capacitor is charged by connecting it across a battery of emf \(E_{0}\)
(B) Dielectric of dielectric constant \(K\) and thickness d is inserted
(C) C apacitor is disconnected from battery
(D) Separation between plates is doubled

|Column-I (Steps performed) |Column-II (Final value of Q uantity (Symbols have usual meaning) (Steps performed)|
|-----|------|
|(a) \((A)(D)(C)(B)\)|(p) \(Q=\frac{C_{0} E_{0}}{2}\)|
|(b) (D)(A)(C)(B)|(q) \(Q=\frac{K C_{0} E_{0}}{K+1}\)|
|(c) \((B)(A)(C)(D)\)|(r) \(C=\frac{K C_{0}}{K+1}\)|
|(d) \((A)(B)(D)(C)\)|(s) \(V=\frac{E_{0}(K+1)}{2 K}\)|

1 \(a-p, r, s, b-p, r, s, c-r, d-q, r\)
2 \(a-p, b-p,r c-r, d-q,\)
3 \(a-p,s, b-r,s, c-r, d-q,\)
4 \(a-r, s, b-s, c-r, d-q, r\)
Electrostatic Potentials and Capacitance

268051 In the circuit, both capacitors areindentical. C olumn I indicates action done on capacitors 1 and Column II indicates effect on capacitor 2

1 \(ar, b-p,q, c-s, d-p,q\)
2 \(arr, b-p, c-s, d-q\)
3 \(a-r, b-p, c-r, d-q\)
4 \(a-s, b-q, c-s, d-q\)
Electrostatic Potentials and Capacitance

268052 The potential across a\(3 \mu \mathrm{F}\) capacitor is \(12 \mathrm{~V}\) when it is not connected to anything. It is then connected in parallel with an uncharged \(6 \mu \mathrm{F}\) capacitor. At equilibrium, the charge and potential difference across the capacitor 3 \(\mu \mathrm{F}\) and \(6 \mu \mathrm{F}\) arelisted in column I. M atch it with column III.
|Column-I|Column-II|
|------|------|
|(a) charge on \(3 \mu \mathrm{F}\) capacitor|(p) \(12 \mu \mathrm{C}\)|
|(b) charge on \(6 \mu \mathrm{F}\) capacitor|(q) \(24 \mu \mathrm{F}\)|
|(c) potential difference across \(3 \mu \mathrm{F}\) |(r) \(8 \mathrm{~V}\) capacitor|
|(d) potential difference across \(6 \mu \mathrm{F}\) |(s) \(4 \mathrm{~V}\) capacitor|

1 ar, b-p, c-s, d-q
2 a-p, b-q, c-s, d-s
3 ar, b-p, c-q, d-q
4 arr, b-q, c-s, d-q