Question

In a CE transistor, a change of $8.0 \text{ mA}$ in the emitter current produces a change of $7.8 \text{ mA}$ in the collector current. What change in the base current is necessary to produce the same change in the collector current?

• A. $200 \; \mu\text{A}$
• B. $50 \; \mu\text{A}$
• C. $100 \; \mu\text{A}$
• D. $150 \; \mu\text{A}$

Hint:

Always keep this rule in mind: The base current is a tiny bottleneck gate current, representing the difference between the large outer currents ($I_B = I_E - I_C$). Simply subtracting the coefficients ($8.0 - 7.8 = 0.2$) instantly gives you the fraction needed to match the options.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem presents a bipolar junction transistor connected in a Common Emitter (CE) configuration. Given the simultaneous changes in the emitter current ($\Delta I_E$) and collector current ($\Delta I_C$), we need to find the corresponding change required in the base current ($\Delta I_B$).

Step 2: Key Formula or Approach:
According to Kirchhoff's Current Law applied to a transistor structure, the total current entering the device must balance the currents exiting it. This gives the fundamental relationship:
$$I_E = I_B + I_C$$ Differentiating or taking changes on both sides yields:
$$\Delta I_E = \Delta I_B + \Delta I_C$$

Step 3: Detailed Explanation:
We are given the following variations:
Change in emitter current, $\Delta I_E = 8.0 \text{ mA}$
Change in collector current, $\Delta I_C = 7.8 \text{ mA}$
Rearranging the current relation equation to isolate the base current change ($\Delta I_B$):
$$\Delta I_B = \Delta I_E - \Delta I_C$$ Substitute the given numerical parameters:
$$\Delta I_B = 8.0 \text{ mA} - 7.8 \text{ mA} = 0.2 \text{ mA}$$ The options are given in microamperes ($\mu\text{A}$). Since $1 \text{ mA} = 1000 \; \mu\text{A}$, let's convert the units:
$$\Delta I_B = 0.2 \times 1000 \; \mu\text{A} = 200 \; \mu\text{A}$$

Step 4: Final Answer:
The required change in the base current is $200 \; \mu\text{A}$, which corresponds to option (A).