MHTCET 14 May 2023 Shift 1 Solved Paper

In a common emitter configuration, the parameters ' $\alpha$ ' (alpha) and ' $\beta$ ' (beta) are related as follows:$\alpha$ is the current gain in a common base configuration and $\beta$ is the current gain in a common emitter configuration. The relationships between ' $\alpha$ ' and ' $\beta$ ' are given by:$\beta=\frac{\alpha}{1-\alpha}$and$\alpha=\frac{\beta}{\beta+1}$Let's examine the given options one by one to determine the incorrect relation: Option A: $\frac{1}{\alpha}=\frac{1}{\beta}+1$Rewriting this equation:$\frac{1}{\alpha}=\frac{1}{\beta}+1$This can be written as:$\frac{1}{\alpha}=\frac{1+\beta}{\beta}$Therefore, this is a correct relation.Option $\text{B}: \alpha=\frac{\beta}{1-\beta}$We know that:$\alpha=\frac{\beta}{\beta+1}$Clearly, $\frac{\beta}{1-\beta}$ does not match this, so this is the incorrect relation. Option $\text{C}: \alpha=\frac{\beta}{1+\beta}$We know that:$\alpha=\frac{\beta}{\beta+1}$This is the correct relation. Option D: $\frac{1}{\beta}=\frac{1}{\alpha}-1$Rewriting this equation:$\frac{1}{\beta}=\frac{1}{\alpha}-1$This can be written as:$\frac{1}{\beta}=\frac{1-\alpha}{\alpha}$ From the relation $\beta=\frac{\alpha}{1-\alpha}$, inverting both sides we get:$\frac{1}{\beta}=\frac{1-\alpha}{\alpha}$Therefore, this is a correct relation.In conclusion, the incorrect relation between ' $\alpha$ ' and ' $\beta$ ' is Option $\text{B}: \alpha=\frac{\beta}{1-\beta}$.