Question

The current gain of a transistor in common base mode is 0.99. To change the emitter current by \(5 \mathrm{~mA}\). What will be the necessary change in collector current ? (A) \(5.1 \mathrm{~mA}\) (B) \(4.95 \mathrm{~mA}\) (C) \(2.45 \mathrm{~mA}\) (D) \(0.196 \mathrm{~mA}\)

Short answer

The necessary change in collector current is \(4.95 \mathrm{~mA}\).

Step-by-step solution

Understand the given data and formula

We are given the common base current gain, represented by \(\alpha\), which is 0.99. We are asked to find the change in collector current, \(\Delta I_C\), for a change in emitter current of \(\Delta I_E = 5 \mathrm{~mA}\). The relationship between collector current, emitter current and base current in a common-base configuration transistor is given by the formula: \(I_E = I_C + I_B\). Since we have the current gain, we can use the formula \(\alpha = \frac{I_C}{I_E}\) to relate the change in collector current to the change in emitter current.

Determine the change in collector current based on emitter current change and current gain

We want to determine the necessary change in collector current, \(\Delta I_C\), when the emitter current, \(\Delta I_E\), changes by \(5 \mathrm{~mA}\). Using the current gain formula, we can write: \[\Delta I_C = \alpha \cdot \Delta I_E\] Now, plug in the given values, \(\alpha = 0.99\) and \(\Delta I_E = 5 \mathrm{~mA}\): \[\Delta I_C = 0.99 \cdot 5 \mathrm{~mA}\]

Calculate the final answer

Now perform the multiplication: \[\Delta I_C = 4.95 \mathrm{~mA}\] So, the necessary change in collector current is \(4.95 \mathrm{~mA}\). Therefore, the correct answer is (B) \(4.95 \mathrm{~mA}\).