The nominal quiescent collector current of a transistor

The nominal quiescent collector current of a transistor is 1.2 mA. If the range of β for this transistor is 80 ≤ β ≤ 120 and if the quiescent collector current changes by ± 10 per cent, the range in value for r_π is:

1. 1.73 kΩ < r_π < 2.59 kΩ
2. 1.93 kΩ < r_π < 2.59 kΩ
3. 1.73 kΩ < r_π < 2.59 kΩ
4. 1.56 kΩ < r_π < 2.88 kΩ

Given that, I_CQ = 1.2 mA ± 10%

i.e., I_{CQ min} =		1.2 –	1.2 × 10		= 1.08 mA
			100

80 ≤ β ≤ 120 I_{CQ max} =		1.2 +	1.2 × 10		= 1.32 mA
			100

i.e. β_max = 120 and β_min = 80
we know that,

r_π =	β	=	β·V_T
	g_m		I_CQ

r_{π max} =	β_max · V_T
	I_{CQ min}

=	120 × 26 × 10^–3	= 2.88 kΩ
	1.08 × 10^–3

r_{π min} =	β_min ·V_T
	I_{CQ max}

=	80 × 26 × 10^–3	= 1.56 kΩ
	1.32 × 10^–3

Hence alternative (D) is the correct choice.