Part 1 SAQ 1 (ENGR5001)

Part 1 SAQ 1Exercise sheetCurrent spec2:212 min

ENGR5001 Part 1 Self-Assessment Questions, Q1

Develop a linear time invariant model showing the relationship between the input voltage $V_i$ and output voltage $V_o$ for the RLC network below (inductor $L$ and resistor $R$ in series, output taken across the capacitor $C$ ).

What assumptions have you made? Put the equation obtained into the standard form, indicating the steady state gain, damping ratio, natural frequency, forcing function and/or time constant.

RLC network: L and R in series from the input V_i, output V_o across C.

Formulas you may need

Inductor $V_L = L\dfrac{di}{dt}$ ; resistor $V_R = Ri$ ; capacitor $i = C\dfrac{dV_C}{dt}$ ; Kirchhoff's voltage law (learn this)
Generalised second order form $\dfrac{d^2x}{dt^2} + 2\zeta\omega_n\dfrac{dx}{dt} + \omega_n^2 x = Ku(t)$ , steady state gain $K/\omega_n^2$ (learn this)
Generalised first order form $\tau\dfrac{dx}{dt} + x = Ku(t)$ (learn this)