The capacitors in each circuit are fully charged before the switch is closed. Rank, from longest to shortest, the length of time

solution:

the spring force applied by a spring with spring constant k can be expressed as

where k acts as the spring constant

and x indicates the spring's deformation

to determine the work completed by the spring

the amount of work done by the spring when moving from x=0 to x=L

substituting the limits x=0 and x=L

we derive the work done in terms of k and L

Answer:

a) Q = C*emf

b)  Decrease in electric field strength and electric potential

c) Initial current through the resistor = emf/R

d) The final charge = K*C*emf

Explanation:

a) The resistors and capacitors are linked in series with the battery

According to Kirchoff's voltage law, the total voltage in the circuit must equal zero

Let represent the Voltage across the Resistor

and

Integrating and into equation (1)

Initially, as the capacitor reaches full charge, the current will drop to zero because of equilibrium

b) When the plastic sheet is inserted between the plates, current begins to flow because both the electric field intensity and electric potential decrease. As a result, charge diminishes, leading to current flow

c) The current through the resistor equates to the total current within the circuit (given the series connection)

Substituting the values of t and I₀ into the aforementioned formula for I

d) Note: The initial charge on the capacitor equals C * emf

Following the insertion of the plastic, the new charge will be: