DC Transients

«««< HEAD #### Learning objectives of the lecture

• DC transients
• Current growth and decay in LR and RC circuits
• Integrator and Differentiator circuits

Introduction

======= > # Learning objectives > >* DC transients >* Current growth and decay in LR and RC circuits >* Integrator and Differentiator circuits

Introduction

909c1836775a43123028537885ce20ffccba239f If a D.C. voltage source is connected in series to a circuit with inductance L and resistance R, there is a short period of time immediately after the voltage is connected during which the current flowing in the circuit and the voltages across L and R are changing. The same occurs when a capacitor C and resistor R are connected in series. These changes in voltage are calles transient . Note: The proofs for the following equations may (probably will) be asked for during the exam. The lecture notes on Keats clearly show every steps to follow.

Current growth in LR

Three different equations are to be remembered concerning the current growth in a circuit with inductance and resistance in series. For a LR circuit, $\tau$ is defined as follows: $\tau=\frac{L}{R}$ $I(t)=\frac{V}{R}(1-exp(-\frac{t}{\tau}))$ $V_L(t) =L\frac{dI(t)}{dt}=V \times exp(-\frac{-t}{\tau})$ $V_R(t)=I(t )\times R= V(1-exp(-\frac{-t}{\tau}))$

Current decay in LR circuit

Similarly to the current grow, three equations need to be remembered For a LR circuit, $\tau​$ is defined as follows: $\tau=\frac{L}{R}​$

Charching a capacitor

Four equations need to be remembered when it comes to charging a capacitor. In an RC circuit, $\tau$ is defined as follows : $\tau= RC$

Discharging a capacitor

Similarly to the charge of a capacitor, four equations need to be remembered In an RC circuit, $\tau\ $ is defined as follows : $\tau$= RC

$V_C(t)=V(exp(-\frac{-t}{\tau})$ $Q_C(t)=C \times V_C(t)$ $V_R(t)=V_C(t)$ $I(t)=\frac{V_R(t)}{R}=\frac{V}{R}exp(-\frac{t}{\tau})$