Answer:
A
The energy dissipated in the resistor
B
The energy dissipated in the resistor
Explanation:
In order to gain a good understanding of the solution above it is necessary to understand that the concept required to solve the question is energy stored in the parallel plate capacitor.
Initially, take the first case. In that, according to the formula for energy stored in parallel plate capacitor with the dielectric inserted between the two plates, find the energy stored. Then, find the energy stored in the parallel plate capacitor when no dielectric is present. Then, write the equation of energy stored in the capacitor with the dielectric present in the form of the energy stored in the capacitor without the dielectric present. The equation must not be in the form of voltage as battery is removed in this case.
For part B, use the equation of the energy dissipated in the resistor. Write it in the form of the equation for energy stored in the parallel plate capacitor without dielectric in it. The equation must be in the form of voltage as battery is kept connected. Looking at the fundamentals
The energy stored in the parallel plate capacitor with the dielectric is given by,
Here, the energy stored in the capacitor will be equal to the energy dissipated in the resistor. In this equation, Uk is the energy dissipated in the resistor, q is charge, k is the dielectric constant, and C is the capacitance.
Now, the equation of the energy stored in the parallel plate capacitor without dielectric is,
In this equation, U is the energy stored in the parallel plate capacitor without dielectric, q is charge, and C is the capacitance.
For part B, the battery is still connected. Thus, the equation is used to modify the above equation.
Thus, the energy stored in the parallel plate capacitor with the dielectric is given by,
In this equation, is the energy dissipated in the resistor, V is voltage, k is the dielectric constant, and C is the capacitance.
The equation of the energy stored in the parallel plate capacitor without dielectric is,
In this equation, U is the energy dissipated in the resistor, V is voltage, k is the dielectric constant, and C is the capacitance.
(A)
The equation for energy dissipated in the resistor is,
Substitute in the equation of
Note :
If the resistance relates to the capacitor, the energy stored in the capacitor is dissipated through the resistance. Thus, by substituting the equation of U, the expression is found out.
(B)
The equation for energy dissipated in the resistor is
Here, V is voltage in the circuit.
Substitute in the equation of
So,