ENGR201 2019 B3 (ENGR5001)

ENGR201 2019 B3Past paperOld spec ENGR2012:225 marks30 min

The circuit shown in Figure B3-1 consists of a resistor $R$ and an inductor $L$ connected in series with a voltage source $V(t)$ .

Formulas you may need

$v_R = Ri$ , $v_L = L\dfrac{di}{dt}$ , Kirchhoff's voltage law (learn this)
$\mathcal{L}\left[\dfrac{di}{dt}\right] = sI(s) - i(0)$ (learn this; printed in the ENGR201 Laplace table)
$\sin\omega t \leftrightarrow \dfrac{\omega}{s^2 + \omega^2}$ , $\cos\omega t \leftrightarrow \dfrac{s}{s^2 + \omega^2}$ , $e^{-\alpha t} \leftrightarrow \dfrac{1}{s + \alpha}$ (learn this; printed in the ENGR201 Laplace table)
Partial fractions with an irreducible quadratic: $\dfrac{A}{Ls + R} + \dfrac{Bs + C}{s^2 + 1}$ (learn this)

(a)
Write down a differential equation describing the rate of change of current $i(t)$ with time, explaining the origin of each term in your answer.
[7]Third
(b)
Using Laplace transformation methods, derive an expression describing the current response $I(s)$ in terms of the voltage stimulus $V(s)$ , given that $i(0) = 0$ .
[8]Third
(c)
If the voltage source is given by $V\sin(t)$ , derive an expression for the current response $i(t)$ .
[10]