devarshi-dt-logo

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 120V. Calculate the value of R to make the bulb light up 5s after the switch has been closed (log₁₀2.5=0.4).

3.3×10⁷Ω

1.3×10⁴Ω

1.7×10⁶Ω

2.7×10⁶Ω

Solution:

V=V₀(1−e⁻ᵗ/RC)
120=200(1−e⁻⁵/R×2×10⁻⁶)
0.6=1−e⁻⁵/R×2×10⁻⁶
0.4=e⁻⁵/R×2×10⁻⁶
ln(0.4)=−5/R×2×10⁻⁶
−0.916=−5/R×2×10⁻⁶
R=5/(0.916×2×10⁻⁶)
R=2.73×10⁶Ω≈2.7×10⁶Ω