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# Lab10 - Lab 10 Capacitors and inductors in AC circuits and...

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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) MT65 MT86 MT67 MT86MT40MT116MT41 MT116 MT73MT40MT116MT41 MT116 MT84MT47MT50 MT84 MT84MT47MT50 MT84 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 tends to zero since the current through the capacitor ( C dV dt ) increases with frequency.

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

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