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VC is the ideal voltmeter in the figure....

`V_C` is the ideal voltmeter in the figure. Resistance of the resistor shown is R. Initially the switch is in position 2 when charging of the capacitor starts. Initially the capacitor was uncharged. The switch in circuit shifts automatically from 2 to 1 when `V_C gt 2V//3` and goes back to 2 from 1 when `V_C lt V//3`. The ideal voltmeter reads voltage across capacitor as plotted. What is the period T of the wave from in terms of R and C ?
,

A

`3RC 1n 3 `

B

`2 RC 1 n 2`

C

`(RC//2)1n 2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
b. `t_1` is the time of capacitor to discharge from `2V//3` to `V//3`.
For this , `V/3 = (2V)/2 e^(-t_1//tau)` or `t_1 = tau1n 2 = RC 1n2`
`t_2` is time for charging of capacitor
from `V//3 "to" 2V//3`.
So `int_(VC//3)^(2VC//3) (dq)/(VC-q) = int_(0)^(t_2) (dt)/(RC)`
or `t_2= RC1n 2`
`T = t_1 + t_2 = 2RC 1n 2 `
.
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