A resistor 'R' and 2µF capacitor in series is connected through a switch to 200V 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. (log10 2.5 = 0.4)

Engineering

Physics

RC Circuit

Question

A resistor 'R' and 2µF capacitor in series is connected through a switch to 200V 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. (log₁₀ 2.5 = 0.4)

1.7 × 10⁵ $Ω$

2.7 × 10⁶ $Ω$

3.3 × 10⁷ $Ω$

1.3 × 10⁴ $Ω$

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v = 200 (1 – e^–t/t)

120 = 200(1 – e^–t/t)

$e^{- t / τ} = \frac{200 - 120}{200} = \frac{80}{200}$

t/t = log(2.5) = 0.4

5 = (0.4) × R × 2 × 10^–6

$\Rightarrow R = \frac{5}{(0.4) \times 2 \times 10^{- 6}}$

= R = 2.7 × 10⁶