Question

A resistor $R$ and $2\mu F$ capacitor in series is connected through a switch to $200$ $V$ direct supply. Across the capacitor is a neon bulb that lights up at $120$ $V$. Calculate the value of $R$ make the bulb light up $5$ $s$ after the switch has been closed $({\log }_{10}2.5=0.4).$

• A. $1.3\times {10}^4\Omega$
• B. $1.7\times {10}^6\Omega$
• C. $2.7\times {10}^6\Omega$
• D. $3.3\times {10}^7\Omega$

Answer 1

The correct option is C $2.7\times {10}^6\Omega$

$V=V_0(1-e^{\frac{-t}{RC}})$
$120=200(1-e^{\frac{-5}{R\times 2\times {10}^{-6}}})$
$R=\frac{5}{2\times 0.4\times 2.303\times {10}^{-6}}\approx 2.7\times {10}^6\Omega$