SATHEE: Electrostatics Question 546

Electrostatics Question 546

Question: The capacities of two conductors are $C_{1}$ and $C_{2}$ and their respective potentials are $V_{1}$ and $V_{2}$ . If they are connected by a thin wire, then the loss of energy will be given by [MP PMT 1986]

Options:

A) $\frac{C_{1} C_{2} (V_{1} + V_{2})}{2 (C_{1} + C_{2})}$

B) $\frac{C_{1} C_{2} (V_{1} - V_{2})}{2 (C_{1} + C_{2})}$

C) $\frac{C_{1} C_{2} {(V_{1} - V_{2})}^{2}}{2 (C_{1} + C_{2})}$

D) $\frac{(C_{1} + C_{2}) (V_{1} - V_{2})}{C_{1} C_{2}}$

Show Answer

Answer:

Correct Answer: C

Solution:

Initial energy

$U_{i} = \frac{1}{2} C_{1} V_{1}^{2} + \frac{1}{2} C_{2} V_{2}^{2}$ ,

Final energy $U_{f} = \frac{1}{2} (C_{1} + C_{2}) V^{2}$ (where $V = \frac{C_{1} V_{1} + C_{2} V_{2}}{C_{1} C_{2}})$

Hence energy loss $Δ U = U_{i} - U_{f} = \frac{C_{1} C_{2}}{2 (C_{1} + C_{2})} {(V_{1} - V_{2})}^{2}$

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Electrostatics Question 546

Question: The capacities of two conductors are C1 and C2 and their respective potentials are V1 andV2 . If they are connected by a thin wire, then the loss of energy will be given by [MP PMT 1986]

Options:

Answer:

Solution:

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Question: The capacities of two conductors are $C_{1}$ and $C_{2}$ and their respective potentials are $V_{1}$ and $V_{2}$ . If they are connected by a thin wire, then the loss of energy will be given by [MP PMT 1986]