question_answer

For a common emitter transistor amplifier, the audio-signal voltage across the collector resistance of \[2\,k\,\Omega ,\] is 2 V. If the current amplification factor of the transistor is 100, calculate (i) base current, (ii) input signal voltage and (iii) power gain. Given that the value of the base resistance is \[1\,k\,\Omega .\]

Answer:

(i) \[{{10}^{-5}}A\]      (ii) \[{{10}^{-\,2}}\,V\] (iii) \[2\times {{10}^{4}}\] Given, \[{{R}_{C}}=2k\,\Omega \] and \[{{I}_{C}}{{R}_{C}}=2\,V\] \[\Rightarrow \]   \[{{I}_{C}}=\frac{2}{{{R}_{C}}}=\frac{2}{2000}={{10}^{-\,3}}A\] Given,   \[\beta =100\] Current gain, \[\beta ={{I}_{C}}\,/\,{{I}_{b}}\]

(i) \[{{I}_{b}}=\frac{{{I}_{C}}}{\beta }=\frac{{{10}^{-\,3}}}{100}={{10}^{-\,5}}A\]

(ii) Input voltage, \[{{V}_{i}}={{l}_{b}}{{R}_{b}}={{10}^{-\,5}}\times {{10}^{3}}={{10}^{-\,2}}V\]

(iii) Power gain, \[{{A}_{p}}={{\beta }_{av}}\times {{A}_{v}}\]

Voltage gain, \[{{A}_{v}}=\frac{{{V}_{o}}}{{{V}_{i}}}=\frac{{{I}_{c}}{{R}_{c}}}{{{I}_{b}}{{R}_{c}}}=\frac{2}{{{10}^{-\,2}}}=200\] \[\therefore \] Power gain \[{{A}_{p}}=\beta \times {{A}_{v}}=100\times 200=2\times {{10}^{4}}\]