An initially air-filled capacitor of capacitance C is filled with dielectric constant k and connected to an ideal battery of emf V via resistance R. At steady state the dielectric is suddenly removed. The heat later produced in R is (1/a) CV²(k−1)ᵇ. Find a+b.
Physics · Mixed Chapter
JEE Mains

Question

An initially air-filled capacitor of capacitance C is filled with dielectric constant k and connected to an ideal battery of emf V via resistance R. At steady state the dielectric is suddenly removed. The heat later produced in R is (1/a) CV²(k−1)ᵇ. Find a+b.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Explanation: Before removal Qᵢ=kCV, while the final steady-state charge is Q𝒻=CV. Right after removal, the voltage is kV, so the voltage difference driving the resistor is (k−1)V. The dissipated heat is ½C[(k−1)V]²=½CV²(k−1)². Thus a=2, b=2 and a+b=4.