Electrostatics Question 284

Question: A fully charged capacitor has a capacitance ?C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass ?m. If the temperature of the block is raised by ?$ \Delta T $ ?, the potential difference v across the capacitance is [AIEEE 2005]

Options:

A) $ 4kV $

B) $ 6kV $

C) $ 8kV $

D) $ 10kV $

Show Answer

Answer:

Correct Answer: C

Solution:

As $ Q=CV,{{( {Q _{\text{1}}} )} _{\text{max}}}=\text{1}{{0}^{\text{6}}}\times \text{6}\times \text{1}{{0}^{\text{3}}}=\text{ 6}mC $

While $ {{( {Q _{\text{2}}} )} _{\text{max}}}=\text{3}\times \text{1}{{0}^{\text{6}}}\times \text{4}\times \text{1}{{0}^{\text{3}}}=\text{12}\mu C $

However in series charge is same so maximum charge on C2 will also be 6 mC (and not 12 mC) and potential difference across it $ {V _{\text{2}}}=\text{ 6}\mu C/\text{3}\mu F=\text{2}KV $ and as in series $ V={V _{\text{1}}}+{V _{\text{2}}} $ so $ {V _{\text{max}}}=\text{ 6}KV+\text{ 2}KV=\text{ 8}KV $



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