Question

A condenser of capacitance $C$ is fully charged by a $200\,V$ 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 block 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)

Given that
$ V =200\, V $
$m =100 \,g=0.1 \,kg $
s $=250 \,Jkg ^{-1} K ^{-1} 4$
$\Delta \theta =0.4 K$
$C =?$
The energy stored in the capacitor is given by
$U =\frac{1}{2} C V^{2} $
$=\frac{1}{2} C \times(200)^{2} $
$=2 C \times 10^{4} \,J$
This energy is used to heat up the block. Let $\Delta \theta$ be the rise in temperature, then heat energy is given by
$Q=m s \Delta \theta =0.1 \times 2.50 \times 0.4 $
$=10\, J$
Now,
$2 C \times 10^{4}=10$
$\Rightarrow C=\frac{10}{2 \times 10^{4}}=5 \times 10^{-4}$
$\therefore C=500\, \mu F$