Consider the circuit shown in the figure Capacitors A and B ,each have capacitance C=2 F The plates - Physics - Current Electricity

Question

Consider the circuit shown in the figure Capacitors A and B
,each have capacitance C=2 F The plates of capacitor A are shorted
using a wire of resistance R =1 ohm while the left plate of
capacitor B is given an initial charge Q=+4C The switch is closed
at time t=0 What will be the initial current drawn from the battery
immediately after the switch is closed?

Somnath physics · Accepted Answer

Let q be the charge flow from the cell at time t.

Solving mesh 1

i₁ - q/C = 0

=> i₁ = ½q ---1.

Solving mesh 2

i + i₁ + (q+4)/C = E ---2.

=> i + q + 2 = 4×4/2 = 8

=> i + q = 6

At time t = 0 no charge will build up so q = 0

=> i = 6 A

Mathematically lets see this result

=> dq/dt + q = 6