GATE EC 2015 Set 1 — Question 52
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Question
In the circuit shown, mA and mA. Transistors and are identical. Assume that the thermal voltage is 26 mV at 27 °C. At 50 °C, the value of the voltage (in mV) is
Correct answer
83.5 to 84
Solution
The voltage across a diode (or base-emitter junction of a a BJT) is given by , where is the thermal voltage and is the reverse saturation current.
For identical transistors and , their reverse saturation currents are the same.
The voltage is across and is across .
So, and .
The voltage difference .
Given mA and mA.
So, .At 27 °C, mV.
The thermal voltage is directly proportional to absolute temperature .
.
Temperature in Kelvin:
K
KThe thermal voltage at 50 °C () can be calculated as:
.Now, calculate at 50 °C using :
.
.
.The value of is approximately 83.88 mV. This falls within the range 83.5 to 84.0.
For identical transistors and , their reverse saturation currents are the same.
The voltage is across and is across .
So, and .
The voltage difference .
Given mA and mA.
So, .At 27 °C, mV.
The thermal voltage is directly proportional to absolute temperature .
.
Temperature in Kelvin:
K
KThe thermal voltage at 50 °C () can be calculated as:
.Now, calculate at 50 °C using :
.
.
.The value of is approximately 83.88 mV. This falls within the range 83.5 to 84.0.
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