The capacities of two capacitors are C1 and C2 and their respective potentials are V1 and V2 . If they are connected by a thin wire, then the loss of energy will be given by

Question

The capacities of two capacitors are C1 and C2 and their respective potentials are V1 and V2 . If they are connected by a thin wire, then the loss of energy will be given by (A) (C1 C2(V1+V2)/2(C1+C2)) (B) (C1 C2(V1-V2)/2(C1+C2)) (C) (C1 C2(V1-V2)2/2(C1+C2)) (D) ((C1+C2)(V1-V2)/C1 C2)

Tardigrade Admin · Accepted Answer

Initial energy, Ui=(1/2) C1 V12+(1/2) C2 V22 . Final energy Uf=(1/2)(C1+C2) V2(. where .V=(C1 V1+C2 V2/C1 C2)) Hence, energy loss, Δ U=Ui-Uf=(C1 C2/2(C1+C2))(V1-V2)2

Q. The capacities of two capacitors 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

$\frac{C _{1} C _{2} ( V _{1} + V _{2} )}{2 ( C _{1} + C _{2} )}$

$\frac{C _{1} C _{2} ( V _{1} - V _{2} )}{2 ( C _{1} + C _{2} )}$

$\frac{C _{1} C _{2} ( V _{1} - V _{2} ) ^{2}}{2 ( C _{1} + C _{2} )}$

$\frac{( C _{1} + C _{2} ) ( V _{1} - V _{2} )}{C _{1} C _{2}}$

Q. The capacities of two capacitors are C1​ and C2​ and their respective potentials are V1​ and V2​. If they are connected by a thin wire, then the loss of energy will be given by

2(C1​+C2​)C1​C2​(V1​+V2​)​

2(C1​+C2​)C1​C2​(V1​−V2​)​

2(C1​+C2​)C1​C2​(V1​−V2​)2​

C1​C2​(C1​+C2​)(V1​−V2​)​

Initial energy, Ui​=21​C1​V12​+21​C2​V22​. Final energy Uf​=21​(C1​+C2​)V2( where V=C1​C2​C1​V1​+C2​V2​​) Hence, energy loss, ΔU=Ui​−Uf​=2(C1​+C2​)C1​C2​​(V1​−V2​)2

Q. The capacities of two capacitors 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

$\frac{C _{1} C _{2} ( V _{1} + V _{2} )}{2 ( C _{1} + C _{2} )}$

$\frac{C _{1} C _{2} ( V _{1} - V _{2} )}{2 ( C _{1} + C _{2} )}$

$\frac{C _{1} C _{2} ( V _{1} - V _{2} ) ^{2}}{2 ( C _{1} + C _{2} )}$

$\frac{( C _{1} + C _{2} ) ( V _{1} - V _{2} )}{C _{1} C _{2}}$