Question

A Cds cell has a dark resistance of $100k\Omega$ & a resistacne in a light beam of $30k\Omega$. The system to trigger comparator within $10ms$ of the beam interruption is $($ Given $\tau =72ms)$

• A.
• B. None of the above
• C.
• D.

Answer 1

The correct option is C

Given data:
$R_{dark}=$ Cds cell dark resistance $=100k\Omega$
$R_{day}=$ Cds cell day time resistance $=30k\Omega$
$\tau =$ time constant $=72ms$
$R_1\left(t\right)=R_{dark}+(R_{day}-R_{dark})e^{-t/\tau }$
$R_1(t=10ms)=100K+(30K-100K)e^{(-10m/72m)}$
$=100K-70K{e}^{-10/72}$
$R_1(t=10ms)=39.1k\Omega$
To trigger comparactor we required $3V$ at non inverting terminal of the op-amp
So, $3V=\frac{-R_{photocell}}{R_2}\times -1$
$R_2=\frac{39.1}{R_2}k\Omega \cong 13k\Omega$
$R_2=13k\Omega$
So, the correct circuit is option (a) only