Question

A Cds cell has a dark resistance of $120k\Omega$ in day light beam. The time constant is $80msec$, the resistance $($in $k\Omega$) of the cell after $40msec$ of application of a beam is

• A. $62.38$
• B. $100$
• C. $25$
• D. $50.38$

Answer 1

The correct option is A $62.38$

$R_{dark}=$ dark resistance $=120k\Omega$
$R_{day}=$ day light resistance $=25k\Omega$
$\tau =80msec$
We know the relation
$R\left(t\right)=R_{dark}+(R_{day}-R_{dark})e^{(-t/\tau )}$
$R\left(t\right)=120k\Omega +(25k\Omega -120k\Omega )e^{(-t/80m)}$
$=120k\Omega +(-95k\Omega )e^{(-t/80m)}$
$R(t=40msec)=120K-95K{e}^{(-40m/80m)}$
$=62.38\left(k\Omega \right)$