If the collector current changes from 2mA to 3mA in a transistor, when collector-emitter voltage is increased from 2 to 10V, then the output resistance of the transistor is

Options

A. `2 k Omega `
B. `4 l Omega `
C. `6 k Omega `
D. `8 k Omega `

Answer

To find the output resistance of the transistor, we can follow these steps:

### Step 1: Identify the changes in collector current and collector-emitter voltage
- The initial collector current (I1) is 2 mA and the final collector current (I2) is 3 mA.
- The initial collector-emitter voltage (V1) is 2 V and the final collector-emitter voltage (V2) is 10 V.

### Step 2: Calculate the change in collector current (ΔIC)
\[ \Delta I_C = I_2 - I_1 = 3 \, \text{mA} - 2 \, \text{mA} = 1 \, \text{mA} \]
Convert this to amperes:
\[ \Delta I_C = 1 \times 10^{-3} \, \text{A} \]

### Step 3: Calculate the change in collector-emitter voltage (ΔVCE)
\[ \Delta V_{CE} = V_2 - V_1 = 10 \, \text{V} - 2 \, \text{V} = 8 \, \text{V} \]

### Step 4: Use Ohm's Law to find the output resistance (R)
According to Ohm's Law, the output resistance can be calculated using the formula:
\[ R = \frac{\Delta V_{CE}}{\Delta I_C} \]
Substituting the values we calculated:
\[ R = \frac{8 \, \text{V}}{1 \times 10^{-3} \, \text{A}} = 8 \times 10^{3} \, \Omega \]

### Step 5: Convert to kilo-ohms
\[ R = 8 \, \text{k}\Omega \]

Thus, the output resistance of the transistor is **8 kΩ**.