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Chapter 9: Problem 76

The collector current of a transistor is \(3.4 \mathrm{A}\) for a base current of \(4.2 \mathrm{mA}\). What is the current gain?

Short Answer

Expert verified
The current gain (β) of the transistor is approximately 810.

Step by step solution

01

Convert base current into amps

First, we need to convert the base current from milliamps (mA) to amps (A), because the collector current is given in A and we should use the same units. To convert mA to A, we simply divide the value by 1000: Ib (in A) = Ib (in mA) / 1000
02

Calculate the current gain (β)

Now that we have the base current in amps, we can calculate the current gain using the formula: β = Ic / Ib Plugging in the values we have: β = 3.4A / \(4.2 * 10^{-3}\)A
03

Solve for β

Now, we just need to solve for β: β = 3.4A / \(4.2 * 10^{-3}\)A = 809.52
04

Round the result

Finally, we can round the result to an appropriate number of significant figures. In this case, let's round it to the nearest whole number: β ≈ 810 So, the current gain of the transistor is approximately 810.

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