Electric Circuits and Networks

 

EXAMPLE: 11.10-1

A series RLC circuit has L = 10 mH, C = 1000 μF and R = 10 Ω. The capacitor is initially charged with 10 V. Find an expression for the voltage across the capacitor when the circuit is excited by 10 u(t).

SOLUTION

This is a problem that involves both zero-input response and zero-state response. The zero-input response component arises due to the initial voltage across the capacitor. The zero-state response component is nothing but step response scaled by 10.

Zero-lnput Response Component:

Characteristic equation is γ² + 10³ γ + 10⁵ = 0. Natural frequencies of the circuit = –112.7 and –887.3. This is an over-damped circuit.

∴ v_C(t) = A₁ e^–112.7t + A₂ e^–887.3t

and i(t) = 10^–3 × (–112.7 A₁ e^–112.7t – 887.3 A₂ e^–887.3t)

Applying ...