Math Problem Statement

請解答

如下面圖所示,試求電流 I。

Solution

The image you provided shows a transistor circuit. The goal is to calculate the current II flowing through the circuit.

We are given the following:

  • The power supply voltage: VCC=12.7VV_{CC} = 12.7 \text{V}
  • A resistor in series with the collector: 1kΩ1 \text{k}\Omega
  • A resistor in the base: 200kΩ200 \text{k}\Omega
  • A transistor with a current gain (or beta): β=99\beta = 99

Step-by-Step Solution:

  1. Assume Transistor in Active Region: We will assume that the transistor is in active mode. The voltage at the base-emitter junction VBEV_{BE} is approximately 0.7V0.7 \text{V} for a silicon transistor.

  2. Determine the Base Voltage VBV_B: The base voltage is determined by the voltage divider formed by the 200 kΩ resistor and the base-emitter voltage: VB=VCCIBRBβV_B = V_{CC} - \frac{I_B \cdot R_B}{\beta} where ( I_B \approx \frac{12.

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Math Problem Analysis

Mathematical Concepts

Ohm's Law
Transistor Current Relations
Kirchhoff's Voltage Law

Formulas

I = \frac{V}{R}
I_C = \beta \cdot I_B
V_CE = V_{CC} - I_C \cdot R_C

Theorems

Kirchhoff's Voltage Law
Current Gain of a Transistor

Suitable Grade Level

University-level