Question

A 10 V is connected across a load whose V-I characteristics is given by 7I = V^2 + 2V. The internal resistance of the battery is of magnitude 1Ω. The current delivered by the battery is ____________

(a) 6 A

(b) 5 A

(c) 7 A

(d) 8 A

The question was posed to me during an interview for a job.

I need to ask this question from Problems Involving Standard Time Functions topic in portion Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

Right answer is (b) 5 A

Easiest explanation: 7I = V^2 + 2V …………………. (1)

Now, V = 10 – 1 ×I

Putting the value of V in eqt (1), we get,

&I = (10 – I) 2 + 2(10 – I)

Or, I = 100 + I2 – 20I + 20 – 2I

Or, I2 – 29I + 120 = 0…………………. (2)

∴ I = \(\frac{+29 ± \sqrt{29^2 – 4(120)}}{2} = \frac{29 ± 19}{2}\)

I = 5 A, 24 A

Now, I = 24 A is not possible because V will be negative from eqt (2)

∴ I = 5 A.