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Question
A transistor of α = 0.99 and VBE = 0.7 V is connected in the common-emitter configuration as shown in the figure. If the transistor is in the saturation region, find the value of collector current.
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Solution
Vcc = 12 V
α = 0.99
VBE = 0.7 V
IC =?
Applying Kirchoff’s voltage law,
VBE + (IC + IB) 1k + 10k.IB + (IC + IB) 1k = 12 ………(1)
IB = `"I"_"C"/β`
β = `α/(1 - α) = 0.99/(1 - 0.99)` = 0.99
IB = `"I"_"C"/99`
IC = β IB
IC = 99 IB
IC = `"I"_"C"/99`
VBE = 0.7 V
Substitute in equation (1)
`0.7/10^3 + (99 "I"_"B" + "I"_"B") + 10 "I"_"B" + (99 "I"_"B" + "I"_"B") = 12/10^3`
100 IB + 10 IB + 100 IB = `(12 - 0.7)/10^3`
210 IB = `11.3/10^3`;
IB = 0.054 × 10−3 A
IC = 99 IB = 99 × 0.054 × 10−3 A
IC = 5.34 × 10−3 A
IC = 5.34 mA
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