Question

For the circuit given below, the value of the g11 and g21 are _________________

(a) g11 = –\(\frac{1}{R_1+R_2}\), g21 = \(\frac{R_2}{R_1+R_2}\)

(b) g11 = \(\frac{1}{R_1-R_2}\), g21 = –\(\frac{R_2}{R_1+R_2}\)

(c) g11 = \(\frac{1}{R_1+R_2}\), g21 = \(\frac{R_2}{R_1+R_2}\)

(d) g11 = \(\frac{1}{R_1-R_2}\), g21 = \(\frac{R_2}{R_1-R_2}\)

I got this question in examination.

Origin of the question is Advanced Problems Involving Parameters in chapter Two-Port Networks of Network Theory

Answer 1

The correct option is (c) g11 = \(\frac{1}{R_1+R_2}\), g21 = \(\frac{R_2}{R_1+R_2}\)

To explain I would say: I1 = \(\frac{V_1}{R_1+R_2}\)

Or, g11 = \(\frac{I_1}{V_1}  = \frac{1}{R_1+R_2}\)

By voltage division, V2 = \(\frac{R_2}{R_1+R_2}\)V1

Or, g21 = \(\frac{V_2}{V_1} = \frac{R_2}{R_1+R_2}\).