Question

In the following circuit, the value of Norton’s resistance between terminals a and b are ___________

(a) RN = 1800 Ω

(b) RN = 270 Ω

(c) RN = 90 Ω

(d) RN = 90 Ω

I had been asked this question by my school principal while I was bunking the class.

This intriguing question originated from Norton’s Theorem Involving Dependent and Independent Sources topic in division Useful Theorems in Circuit Analysis of Network Theory

Answer 1

Right option is (d) RN = 90 Ω

Explanation: By writing loop equations for the circuit, we get,

VS = VX, IS = IX

VS = 600(I1 – I2) + 300(I1 – I2) + 900 I1

= (600+300+900) I1 – 600I2 – 300I3

= 1800I1 – 600I2 – 300I3

I1 = IS, I2 = 0.3 VS

I3 = 3IS + 0.2VS

VS = 1800IS – 600(0.01VS) – 300(3IS + 0.01VS)

= 1800IS – 6VS – 900IS – 3VS

10VS = 900IS

For Voltage, VS = RN IS + VOC

Here VOC = 0

So, Resistance RN = 90Ω.