In the circuit shown in the figure, the input voltage $V_i$ is $20 \, V , V_{BE} = 0 $ and $V_{CE} = 0$ .The values of $I_B , I_C$ and $\beta$ are given by

Question

What is the output of a NAND gate when both inputs are HIGH?

Answer 1

To solve the given problem, we need to determine the values of the base current $I_B$, the collector current $I_C$, and the current gain $\beta$ for the transistor circuit. The transistor parameters given are $V_{BE} = 0$ and $V_{CE} = 0$.

Given, input voltage $V_i = 20 \, V$. We need to identify the correct option from the given choices.

Step 1: Understanding the transistor operation under given conditions

In a transistor circuit, the current gain $\beta$ is the ratio of the collector current $I_C$ to the base current $I_B$:

$\beta = \frac{I_C}{I_B}$

Step 2: Analyzing the given options

We will evaluate each option using the formula $\beta = \frac{I_C}{I_B}$ to find which one is consistent with a possible transistor configuration.

Option 1: $I_B = 40 \, \mu A$, $I_C = 10 \, mA$, $\beta = 250$

$\beta = \frac{10 \, mA}{40 \, \mu A} = 250$

This matches with the provided $\beta$, yet it is incorrect because it does not correspond to typical behavior under the conditions $V_{BE} = 0$ and $V_{CE} = 0$.

Option 2: $I_B = 25 \, \mu A$, $I_C = 5 \, mA$, $\beta = 200$

$\beta = \frac{5 \, mA}{25 \, \mu A} = 200$

This calculation is correct but does not fit the given zero-level operation of the transistor.

Option 3: $I_B = 20 \, \mu A$, $I_C = 5 \, mA$, $\beta = 250$

$\beta = \frac{5 \, mA}{20 \, \mu A} = 250$

Again, this does not match the typical behavior under $V_{BE} = 0$.

Option 4: $I_B = 40 \, \mu A$, $I_C = 5 \, mA$, $\beta = 125$

$\beta = \frac{5 \, mA}{40 \, \mu A} = 125$

This fits well with a typical scenario where both $V_{BE} = 0$ and $V_{CE} = 0$, which indicates the transistor is in complete cut-off or saturation.

Conclusion

The correct answer is $I_B = 40 \, \mu A$, $I_C = 5 \, mA$, $\beta = 125$, as it is consistent with the behavior of a transistor that both voltages $V_{BE} = 0$ and $V_{CE} = 0$, indicating a state where minimum or no current flows, reflecting low gain or full saturation.

Answer 2