Question

The relay shown in figure is to be controlled by a photoconductive cell and other figuure is of photocell illumination characteristics


The circut delivers $10mA$ at a $30V$ setting when the cell is illuminated with about $400lm/m^2$. The circuit becomes denergised when the cell is dark. The requried series resistance $R_1$ $($ in $k\Omega )$ & the dark current $($ in $mA)$ respectively

• A. $1,0.3$
• B. $2,0.1$
• C. $2,0.3$
• D. $2,0.5$

Answer 1

The correct option is C $2,0.3$

The cell current corresponding to illumination level of $400lm/m^2$ is $1k\Omega$. The external resistance $R_1$ is
$-30+I(R_1+1k\Omega )=0$
$-30+10\times {10}^{-3}\left(R_{1}k\Omega \right)=0$
$R_1=\frac{30}{10\times {10}^{-3}}-1k\Omega$
$R_1=2k\Omega$
$I_{dark}=$ dark currnet when illumination in minimum i.e., $i\left(1m/m^2\right)$ & the corresponding resistance of photocell is $100k\Omega$
So, the
$I_{dark}=\frac{V}{R_1+R_{dark}}$
$=\frac{30}{2k\Omega +100k\Omega }$
$I_{dark}=0.294\left(mA\right)$
$\cong 0.3\left(mA\right)$