Question

In the circuit shown below the current I(t) for t≥0^+ (assuming zero initial conditions) is ___________

(a) 0.5-0.125e^-1000t A

(b) 1.5-0.125e^-1000t A

(c) 0.5-0.5e^-1000t A

(d) 0.375e^-1000t A

I got this question in unit test.

This interesting question is from Dot Convention in Magnetically Coupled Circuits in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

The correct answer is (a) 0.5-0.125e^-1000t A

Easy explanation: I (t) = \(\frac{1.5}{3}\) = 0.5

LEQ = 15 mH

REQ = 5+10 = 15Ω

L = \(\frac{L_{EQ}}{R_{EQ}}\)

= \(\frac{15 × 10^3}{15} = \frac{1}{1000}\)

I (t) A – (A – B) e^-t = 0.5 – (0.5-B) e^-1000t

= 0.5(0.5 – 0.375) e^-1000t

= 0.5 – 0.125 e^-1000t

I (t) = 0.5-0.125e^-1000t.