The switch in Figure (a) closes when `Vc = 2V//3` and opens when `Vc = V//3`. The voltmeter reads a voltage as plotted in figure (b). What is the period T of the waveform? (take `R_(1) = 6R` and `R_(2) = 3R`, and `ln2 = 0.7` if required)
(a)

Options

A. `12 RC`
B. `8.4 RC`
C. `11 RC`
D. none of these

Answer

B

Explanation

When the switch closes at `V_(c ) = 2 V//3` the capacitor discharges through `R_(2) = 3R`
T (discharge) `= 3RC ln 2` (since the voltage halves).
The charging occurs through `R_(1) + R_(2) = 9R`
T (charge) `= 9RC ln^(2)`
`T = 12 RC ln 2 ~~ 8.4 RC`