Question

The transfer ratio $\beta $ of a transistor is $50$. The input resistance of the transistor, when used in the common-emitter configuration, is $1k\Omega $. The peak value for the collector alternating current for an input peak voltage of $0.01V$ is?
(A) $0.25\mu A$
(B) $0.01\mu A$
(C) $500\mu A$
(D) $100\mu A$

Answer 1

Hint: The current transfer ratio in a common emitter mode is the ratio of collector current to the base current. To solve this problem, we find the base current by dividing the peak value input voltage with the input resistance given in the question. Then we use the current transfer ratio formula to find the peak collector current in the circuit.
Formula used
1. Current transfer ratio in a common emitter configuration $\beta = \dfrac{{{I_c}}}{{{I_b}}}$
Ohms law to find the base current ${V_i} = {I_b}{R_i}$
2. Current transfer ratio is represented by $\beta $
Peak Base current is represented by ${I_b}$
Peak collector current is represented by ${I_c}$
Input peak voltage is represented by ${V_i}$
The input resistance is represented by ${R_i}$

Complete step by step solution:
Using ohm's law we find the peak Base current in the circuit. In the question, we are given the input resistance and the input peak voltage. Using ohm's law for these values we get Base peak current.
$ {V_i} = {I_b}{R_i} $
$ {I_b} = \dfrac{{{V_i}}}{{{R_i}}} $
$ {I_b} = \dfrac{{0.01V}}{{1k\Omega }} = 0.01mA $
$ {I_b} = 0.01mA $
 The ratio of peak collector current to the peak Base current gives us the transfer ratio in a common emitter configuration. The value of the ratio is given in the question and we know the value of Base peak current, substituting the values we get for the answer.
$ \beta = \dfrac{{{I_c}}}{{{I_b}}} $
$ {I_c} = {I_b} \times \beta = 0.01mA \times 50 = 0.5mA $
$ (\because 1mA={10^3}\mu A)$
$ {I_c}=0.5 \times {10^3}\mu A$
 $ {I_c} = 500\mu A $
 Hence the peak collector current in the configuration is ${I_c} = 500\mu A$

Option (C) ${I_c} = 500\mu A$ is the correct answer.

Note:
1. Common emitter transistors are also called common- emitter amplifiers because the emitter of the transistor is common to both the input and output circuit. The input signal is applied across the ground and the base circuit of the transistor.
2. Some of the most common uses of a common emitter transistor are voltage amplification at low frequencies.
3. Common emitter transistors are also used in radio frequency transceiver circuits.