Question

The two capacitors ${{\text{C}}_{\text{1}}}$ and ${{\text{C}}_{\text{2}}}$ are charged to potentials ${{\text{V}}_{1}}$ and ${{\text{V}}_{2}}$ and then connected in parallel. There will be no flow of energy, if:

• A. ${{C}_{1}}{{V}_{1}}={{C}_{2}}{{V}_{2}}$
• B. ${{V}_{1}}={{V}_{2}}$
• C. ${{C}_{1}}=C{{ }_{2}}$
• D. $\frac{{{C}_{1}}}{{{V}_{1}}}=\frac{{{C}_{2}}}{{{V}_{2}}}$

Answer 1

Answer: (B)

${{V}_{1}}={{V}_{2}}$

Answer 2

When a conductor of capacitance C is charged, it acquires a potential
$V=\frac{q}{C}$
When connected in parallel, equivalent capacitance of combination is
$C={{C}_{1}}+{{C}_{2}}$
Also, energy, flow
$\left( E=\frac{1}{2}C{{V}^{2}} \right)$
will not take place, if potential across capacitors is same.