See circuit It has a switch that can be moved to position a

(See circuit). It has a switch that can be moved to position a or e. With both capacitors C1 and C2 initially uncharged, the switch set to the e position and left for a very long time. The switch is then set to position a and left for a long time. R=R1=R3=R4. R2=2R

When set to position e, how long will it take for the capacitor C2 to charge to 85% of its maximum charge?

Solution

When the switch is connected to position e then the circuit behaves like a RC circuit.

In RC circuit ,charge after time t is q = qo [1-e ^-t/RC]

Given charge after time t is q = 85 % of qo        where qo = maximum charge

                                           = 0.85 qo

Substitute this value in above equation you get ,

0.85 qo = qo [1-e ^-t/RC]

0.85 = [1-e ^-t/RC]

e ^-t/RC = 1-0.85

           = 0.15

   -t/RC = ln(0.15)

           = -1.897

    t/RC = 1.897

         t = 1.897 RC

According to problem, Capacitance C = C₂

                                 Resistance R=R4 = R

So, required time t = 1.897 (R)(C₂)