Lab10 - Lab 10: Capacitors and inductors in AC circuits,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Lab 10: Capacitors and inductors in AC circuits, and electrical resonance 1 Introduction Capacitors and inductors can be used to store energy in electrical circuits in the form of electric fields and magnetic fields respectively. This lab will introduce you to the behavior of these elements in alternating current (AC) circuits. The lab will also cover exper- iments associated with the phenomenon of resonance in simple circuits with a resistor, an inductor and a capacitor. Depending on the values of the inductor and capacitor, these circuits can be made to select or respond to specific resonant frequencies. Such circuits are used in radios and television sets to tune to various frequencies or channels. The principle of resonance is widely used in the design of electrical circuits. EXERCISES 1 AND 2 PERTAIN TO THE BACKGROUND CONCEPTS AND EXER- CISES 3 - 5 PERTAIN TO THE EXPERI- MENTAL SECTIONS. 2 Background When a resistor is connected to an AC voltage source, the voltage is given by, V ( t ) = V 0 sin( ωt ) (1) The current through the resistor is simply given by Ohm’s law as, I ( t ) = V 0 R sin ( ωt ) (2) The current has the same frequency ( f = ω 2 π ) and phase as the voltage source. When the AC source is connected to a capacitor C , the charge on the plates of the capacitor is given by, Q ( t ) = CV ( t ) (3) Differentiating equation 3, and using I = dQ dt , we get, I = C dV dt (4) M m ± m²³´ ³ µ²³´ ³ ¶·¸ ¶·¸ Figure 1: Voltage and current in an AC capacitor circuit. The time period T = 1 f Since V = V 0 sin( ωt ), equation 4 gives, I = ωCV 0 cos( ωt ) = ωCV 0 sin( ωt + π 2 ) (5) Equation 5 shows that the capacitor introduces a phase difference between the voltage and current since the current in the capacitor leads the voltage by 90 (figure 1). The quantity ωCV 0 in equation 5 can be identified as the amplitude of the current I 0 . In analogy with Ohm’s law we can write, I 0 = V 0 X C (6) where the impedance X C is the capacitive reactance (measured in ohms), X C = 1 ωC . The impedance is clearly frequency dependent. At high frequencies it
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/25/2010 for the course PHYS 2213 taught by Professor Hor. during the Spring '10 term at Maple Springs.

Page1 / 3

Lab10 - Lab 10: Capacitors and inductors in AC circuits,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online