1 Chapter 6 Capacitance and inductance EMLAB Contents

1 Chapter 6. Capacitance and inductance EMLAB

Contents 2 1. Capacitors 2. Inductors 3. Capacitor and inductor combinations 4. RC operational amplifier circuits 5. Application examples EMLAB

Usage of inductors and capacitors Power supply board inductor 3 capacitor PC motherboard Cell phone inductor capacitor EMLAB

1. Capacitors 4 • Capacitance is defined to be the ratio of charge to voltage difference. • Used to store charges • Used to store electrostatic energy If the voltage difference between the terminals of the capacitor is equal to the supply voltage, net flow of charges becomes zero. EMLAB

Generation of charges : battery 5 Electrons(-) are absorbed. (+) charges are generated Electrons(-) are generated. (+) charges are absorbed. Electrons are generated via electro-chemical reaction. EMLAB

Usage of capacitors 6 • Used to store charges • Used to store electrostatic energy • Slow down voltage variation EMLAB

Type of capacitors 7 EMLAB

Frequently used formulas on capacitors 8 Capacitance : Current : Voltage : Power : Energy : EMLAB

i-υ relation of capacitors 9 EMLAB

Example 6. 2 10 The voltage across a 5 -μF capacitor has the waveform shown in Fig. 6. 4 a. Determine the current waveform. EMLAB

Properties of capacitors 11 • Capacitor voltage cannot change instantaneously due to finite current supply. • In steady state, capacitor behaves as if open circuited. EMLAB

Example 6. 3 12 Determine the energy stored in the electric field of the capacitor in Example 6. 2 at t = 6 ms. EMLAB

Example 6. 4 13 The current in an initially uncharged 4μF capacitor is shown in Fig. 6. 5 a. Let us derive the waveforms for the voltage, power, and energy and compute the energy stored in the electric field of the capacitor at t=2 ms. EMLAB

2. Inductors 14 EMLAB

Two important laws on magnetic field Current 15 B-field Current generates magnetic field (Biot-Savart Law) Current Time-varying magnetic field generates induced electric field that opposes the variation. (Faraday’s law) V B-field EMLAB

16 Biot-Savart Law Faraday’s Law EMLAB

Self induced voltage 17 = • The induced voltage is generated such that it opposes the applied magnetic flux. • The inductor cannot distinguish where the applied magnetic flux comes from. • If the magnetic flux is due to the coil itself, it is called that the induced voltage is generated by self-inductance. EMLAB

Frequently used formulas on inductors 18 Inductance : Voltage : Current : Power : Energy : EMLAB

Properties of inductors 19 • Inductor current cannot change instantaneously due to finite current supply. • In steady state, inductor behaves as if short circuited. EMLAB

Example 6. 5 20 Find the total energy stored in the circuit of Fig. 6. 8 a. EMLAB

Example 6. 6 21 The current in a 10 -m. H inductor has the waveform shown in Fig. 6. 9 a. Determine the voltage waveform. EMLAB

Example 6. 7 22 The current in a 2 -m. H inductor is Determine the voltage across the inductor and the energy stored in the inductor. EMLAB

Example 6. 8 23 The voltage across a 200 -m. H inductor is given by the expression Let us derive the waveforms for the current, energy, and power. EMLAB

Capacitor and inductor specifications 24 Standard tolerance values are ; 5%, ; 10%, and ; 20%. Tolerances are typically 5% or 10% of the specified value. EMLAB

Example 6. 10 25 The capacitor in Fig. 6. 11 a is a 100 -n. F capacitor with a tolerance of 20%. If the voltage waveform is as shown in Fig. 6. 11 b, let us graph the current waveform for the minimum and maximum capacitor values. EMLAB

6. 3 Capacitor and Inductor Combinations 26 = = EMLAB

27 = = EMLAB

6. 4 RC Operational Amplifier Circuits 28 Op-amp differentiator EMLAB

Op-amp integrator 29 EMLAB

Example 6. 17 30 The waveform in Fig. 6. 26 a is applied at the input of the differentiator circuit shown in Fig. 6. 25 a. If R 2=1 kΩ and C 1=2 μF, determine the waveform at the output of the op-amp. EMLAB

Example 6. 18 31 If the integrator shown in Fig. 6. 25 b has the parameters R 1=5 kΩ and C 2=0. 2μF, determine the waveform at the op-amp output if the input waveform is given as in Fig. 6. 27 a and the capacitor is initially discharged. EMLAB