CIRCUIT ELEMENT: CAPACITOR

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1 CIRCUIT ELEMENT: CAPACITOR PROF. SIRIPONG POTISUK ELEC 308 Types of Circuit Elements Two broad types of circuit elements Ati Active elements -capable of generating electric energy from nonelectric energy (chemical, mechanical, nuclear, etc.) e.g. generators, batteries, operational amplifiers Passive elements consume or store energy received from other elements in the circuit i e.g. resistors, capacitors, inductors 1

2 Capacitors consists of two conducting (metal) plates separated by an insulating gap Circuit symbol with reference voltage and current assignment Physics of the Capacitor 2

3 Example If the voltage of 10 V applied to the capacitor induces 25 mc charge on its plates, what is the capacitance of the capacitor in Farads? Physics of the Capacitor 3

4 Physics of the Capacitor The capacitance can be significantly increased by filling the gap between the plates with so-called dielectric materials. +Q +Q Air Dielectric -Q -Q Relative Permittivity of Selected Materials 4

5 Example Determine the plate size of a square parallel-plate air-gap capacitor that has the capacitance of 1 F and plate spacing of 1 mm. Example A parallel-plate capacitor has the plate size of 500 μm 200 μm. The plates are separated by 2 μm thick dielectric film with relative permittivity ε r = 10. What is the capacitance of this capacitor in Farads? 5

6 Physics of the Capacitor Accumulation of charges on the plates is not instantaneous the voltage across the terminals of a capacitor cannot change abruptly Gradual rise or fall in voltage is referred to as the charging and discharging of the capacitor Physics of the Capacitor The transition period known as the transient state During transient, the amount of charge changes with time a flow of electric current As time progresses until V C = V B, charging stops and the steady state is reached with no current flow Capacitor acts like an open circuit to DC voltage Q C = CV C Q = 0 Transient state Steady state Time 6

7 Q C = CV C Q = 0 Transient state Steady state Time I V C V B Time Time Electrical Characteristics v-i characteristics: i dq dv 1 C = C vc ( t) = i dτ + v( to) dt dt C C = The instantaneous power delivered to the capacitor is dv p = vi = Cv d t The energy stored in the capacitor is t w = p( τ ) dτ = C v t o t t o dv d dτ = τ 1 2 Cv 1 t 2 v( t) v( t ) o t o = [ ( t) v ( t )] C v o 7

8 Energy Stored in Capacitor Capacitance is the circuit property that accounts for energy stored in electric fields established by the accumulated charge on both plates The E field is the Coulomb force per unit charge directed from positive to negative charge and distributed as shown Effect of Dielectric on the E field Alignment of dipoles in the dielectric (Polarization) A flow of displacement current The more dipoles the dielectric material contains, the more additional charges it induces on the capacitor plates 8

9 Example Calculate the amount of charge stored on a 3-pF capacitor with 20 V across it. Find also the energy stored in it. Example The voltage across 0.5 nf capacitor changes with time as shown. What is the current through the capacitor? 9

10 Example The current as shown flows through an initially uncharged 1-mF capacitor. Calculate the voltage across it at t = 2 ms and t = 5 ms. Example Obtain the energy stored in each capacitor under DC steady-state state conditions 10

11 For steady-state conditions with DC sources, capacitors behave as open circuits. Series Capacitance Combination 11

12 Parallel Capacitance Combination Example For the circuit shown, find the voltage across each capacitor. 12

13 Electrolytic Capacitors High capacitance per unit volume Only voltages of proper polarity should be applied (polarized capacitors) One plate is oxide-coated metallic aluminum or tantalum immersed in the electrolytic solution 13

14 Ceramic Capacitors (Non-polarized) High-voltage Capacitors 11 kv capacitors Ultra-capacitor battery Capacitor bank 14

15 Variable Capacitors Capacitance of the variable air capacitor is changed by turning the shaft at the end of the unit. Semiconductor technology allows making variable capacitor without moving parts, e.g., semiconductor diode capacitance is controlled by applied voltage 15

ENGR 2405 Chapter 6. Capacitors And Inductors

ENGR 2405 Chapter 6. Capacitors And Inductors ENGR 2405 Chapter 6 Capacitors And Inductors Overview This chapter will introduce two new linear circuit elements: The capacitor The inductor Unlike resistors, these elements do not dissipate energy They