Question

A condenser of capacitance C is fully charged by a 200V supply. It is then discharged through a small coil of resistance wire embedded in thermally insulated block of specific heat 250 J/Kg-K and of mass 100 g. If the temperature of the book rises by 0.4 K, then the value of C is

• A. 300 $\mu$F
• B. 200 $\mu$F
• C. 400 $\mu$F
• D. 500 $\mu$F

Answer 1

Answer: (D)

500 $\mu$F

The energy stored in the capacitor
$U=\frac{1}{2}C{V}^2=\frac{1}{2}C\times (200{)}^2=2C\times {10}^{4}J$
This energy is used to heat up the block. Let $\Delta \theta$ be the rise in temperature, then heat energy
$Q=ms\Delta \theta =0.1\times 250\times 0.4=10J$
Now,
$2C\times {10}^4=10$
$\Rightarrow C=\frac{10}{2\times {10}^4}=5\times {10}^{-4}=500\mu F$