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Chapter 20: Problem 60

The current gain of a transistor in common emitter circuit is 40 . The ratio of emitter current to base current is (A) 40 (B) 41 (C) 42 (D) 43

Short Answer

Expert verified
The ratio of emitter current to base current in a transistor with a current gain of 40 in a common emitter circuit is 41. So the correct answer is (B) 41.

Step by step solution

01

Understand the relationship between emitter, base, and collector current

In a transistor, the emitter current (I_e) is the sum of the base current (I_b) and the collector current (I_c). Mathematically, this can be written as: \(I_e = I_b + I_c\)
02

Understand the definition of current gain (尾)

The current gain (尾) in a common emitter circuit is defined as the ratio of the collector current (I_c) to the base current (I_b). Mathematically, this can be written as: 尾 = \(\frac{I_c}{I_b}\)
03

Use the given current gain (尾) and rewrite the formula

We are given the current gain as 40. So, we have: 尾 = 40 = \(\frac{I_c}{I_b}\) Now, let's rewrite the formula for the emitter current in terms of the collector current and base current: \(I_e = I_b + I_c\)
04

Replace the collector current (I_c) with the expression in terms of current gain (尾) and base current (I_b)

From Step 3, we have \(I_c = 40 \times I_b\). Now, substituting this expression for I_c in the emitter current formula gives: \(I_e = I_b + (40 \times I_b)\)
05

Simplify the expression for emitter current (I_e) and calculate the ratio \(\frac{I_e}{I_b}\)

Simplifying the expression for I_e, we get: \(I_e = 1 \times I_b + 40 \times I_b = 41 \times I_b\) Now, let's calculate the ratio \(\frac{I_e}{I_b}\): \(\frac{I_e}{I_b} = \frac{41 \times I_b}{I_b} = 41\) So, the ratio of emitter current to base current is 41. The correct answer is (B) 41.

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