In the circuit shown here, the transistor used has a current gain $β = 100.$ What should be the resistance $R_{B}$ so that $V_{C E} = 5 V$ $[neglect V_{B E}]$

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$200 \times 10^{3} Ω$

$500 Ω$

$2 \times 10^{3} Ω$

$1 \times 10^{6} Ω$

answer is A.

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Detailed Solution

Applying Kirchhoff's law to mesh ADCEFA

$V_{C C} = 10 = I_{C} \times 10^{3} + V_{C E} 10 = I_{C} \times 10^{- 3} + 5$

$O r I_{C} = 5 \times 10^{- 3} A . . . . . . (1)$

$I_{b} \times R_{b} + V_{B E} = V_{C C} = 10 V$

$I_{b} \times R_{b} + 0 = 10 . . . . . . . . (2)$

$\sin c e β = 10 = \frac{I_{c}}{I_{b}}; I_{b} = \frac{I_{c}}{100} = \frac{5 \times 10^{- 3}}{100} = 5 \times 10^{- 5} A$

Putting value in (2)

$\begin{array}{l} 5 \times 10^{- 5} \times R_{b} = 10 \\ R_{b} = 2 \times 10^{5} Ω = 200 \times 10^{3} Ω \end{array}$

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