A resistor 'R' and 2μF capacitor in series is connected through

A resistor 'R' and 2μF capacitor in series is connected through a switch to 20 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5s after the switch has been closed. (log102.5 = 0.4)

  1. 2.7 x 106 Ω
  2. 1.3 x 104 Ω
  3. 1.7 x 105 Ω
  4. 3.3 x 107 Ω

Answer

v = 200(1 - e-t/τ)

120 = 200(1 - e-t/τ)

e-t/τ = (200 - 120)/200 = 80/200

-t/τ = log(2.5) = 0.4

5 = 0.4 x R x 2 x 10-6

R = 5/(0.6 x 2 x 10-6)

R = 2.7 x 106

The correct option is A.