Question

In a transistor, a change of \(8.0 \mathrm{~mA}\) in the emitter current produces a change of \(7.8 \mathrm{~mA}\) in the collector current. What change in the base current is necessary to produce the same change in the collector current? (A) \(300 \mu \mathrm{A}\) (B) \(400 \mu \mathrm{A}\) (C) \(200 \mu \mathrm{A}\) (D) \(100 \mu \mathrm{A}\)

Short answer

The change in base current necessary to produce the same change in the collector current is (C) \(200 \mu \mathrm{A}\).

Step-by-step solution

Understand the relationship between emitter, base, and collector currents

In any transistor, the emitter current (I_E) is the sum of the collector current (I_C) and the base current (I_B), as shown by the following equation: \(I_E = I_B + I_C\)

Calculate the initial base current

We have to initially find the base current (I_B) before the change in emitter current. According to the problem, the change in the emitter current (\(ΔI_E\)) is 8.0 mA and the change in the collector current (\(ΔI_C\)) is 7.8 mA. We can use these values to find the change in base current (\(ΔI_B\)): \(ΔI_E = ΔI_B + ΔI_C\) \(ΔI_B = ΔI_E - ΔI_C\) Substituting the given values, \(ΔI_B = 8.0\; mA - 7.8\;mA\)

Calculate the change in base current

Now, compute the change in base current required (\(ΔI_B\)) to produce the same change in collector current: \(ΔI_B = 8.0\; mA - 7.8\;mA\) \(ΔI_B = 0.2\; mA\) Since the options are given in microamperes (μA), we can convert the change in base current from mA to μA: \(ΔI_B = 0.2\; mA * 1000\; (1\; mA = 1000\; μA)\) \(ΔI_B = 200\; μA\)

Identify the correct option

Now that we have calculated the change in base current necessary to produce the same change in the collector current, we can identify the correct option. The answer is: (C) \(200 \mu \mathrm{A}\)