Question

A condenser of capacity $10\mu F$ is charged to a potential of $500V$. Its terminals are then connected to those of an uncharged condenser of capacity $40\mu F$. The loss of energy in connecting them together is:

• A. $1J$
• B. $2.5J$
• C. $10J$
• D. $12J$

Answer 1

The correct option is A $1J$

Initial Energy $=E_i=\frac{1}{2}C{V}^2=\frac{1}{2}10\times {10}^{-6}\times 500\times 500=1.25J$
Total Charge $=CV=10\times {10}^{-6}\times 500=5\times {10}^{-3}$
After connecting the 2 capacitors , Charge remains same .
Effective capacitance $=C_1+C_2=50\times {10}^{-6}$
Voltage across the 2 must be equal .
$5\times {10}^{-3}=50\times {10}^{-6}\times V$
$V=100V$
Final Energy Stored $=E_f=\frac{1}{2}\times 50\times {10}^{-6}\times 100\times 100=0.25J$
Hence Energy Lost =$E_i-E_f$$=1.25J-0.25J=1J$