PHYS 205 Chapter 22, Fall 2017

Chapter 23 Alternating Current Circuits Outline 1. Capacitors and Capacitive Reactance 2. Inductors and Inductive Reactance 3. Circuits Containing Resistance, Capacitance, and Inductance 4. Resonance in Electric Circuits 5. Semiconductor Devices 1- Capacitors and Capacitive Reactance R I V rms rms  The resistance in a purely resistive circuit has the same value at all frequencies. Note: the average value of the current over one cycle is zero! iR and VR are in phase: V = I R Capacitors in an AC Circuit  sin m q V q c V c V t c           Im but cos sin 2 m m dq i c V t I t dt                     m sin V V t   sin 2 m i I t          Not in phase: the voltage lags behind the current by 90o     1 1 CAPACITIVE REACTANCE 2 m C m V X I C C f          Note: if 0 0 No current and C m C C f DC X I V IX        Example 1 A Capacitor in an AC Circuit The capacitance is 1.50μF and the rms voltage is 25.0 V. What is the rms current when the frequency is (a) 100 Hz and (b) 5000 Hz? .0 0236 A 1060 0. V 25 rms rms     XC V I          1060 F .1 50 10 100 Hz 2 1 2 1 6   fC X C (a) (b)          21 2. F .1 50 10 5000 Hz 2 1 2 1 6   fC X C .1 18 A 21.2 0. V 25 rms rms     XC V I In the phasor model, the voltage and current are represented by rotating arrows (called phasors). These phasors rotate at a frequency f. The vertical component of the phasor is the instantaneous value of the current or voltage. Phasor diagram 2- Inductors in an AC Circuit 0 L di V L dt    sin 2 Vm i t L                 sin . cos m m V V i t dt t L L           sin L m di V L V t dt        sin L m V V t   sin 2 Vm i t L            Not in phase: the voltage leads the current by 90o INDUCTIVE REACTANCE Also m m m L m L V V I X L L I V X I           Phasor diagram 3- Circuits containing resistance, capacitance, and inductance = I XL = I XC = I R Phasor diagram Direction of Current Phasor diagram   2 2 TOT L C R V V V V    tan L C R V V V      2 2 L C V I R X X     tan L C X X R       2 2 Total impedance of RLC circuit TOT L C Z R X X      With:   XL L    1 XC C  1 ZC C  ZL L  ZR R  Sum Leads i by 90o In phase with i Lags behind i by 90o Conceptual Example 4 The Limiting Behavior of Capacitors and Inductors The rms voltage of the generator is the same in each case. The values of the resistance, capacitance, and inductance are the same. The frequency of the ac generator is very near zero. In which circuit does the generator supply more rms current? Equivalent to Power in an AC Circuit After 1 cycle, capacitors and inductors do not dissipate energy. They actually store energy during the first half cycle and the same amount during the second half cycle. The only power lost is across the resistor: but cos av R R P IV V V    av P is maximal for cos 1 ; 0     cos cos power factor av P IV     4- Resonance in electric circuits LC 2 1 ƒo     2 2 L C V V I Z R X X       For L C X X  1 L C     0 0 1 1 and 2 f LC LC     Resonant frequency 5- Semiconductor devices Semiconductor devices such as diodes and transistors are widely used in modern electronics. The semiconducting materials (silicon and germanium) used to make diodes and transistors are doped by adding small amounts of an impurity element. n type and p type semiconductors At the junction between the n and p materials, mobile electrons and holes combine and create positive and negative charge layers. The semiconductor diode There is an appreciable current through the diode when the diode is forward biased. Under a reverse bias, there is almost no current through the diode.