Review (Only leave this in if it makes sense) Get white boards out for all this lecture) How long does it take a 5uF capacitor in a series RC circuit to charge to 95% of being fully charged if the resistor is 10,000 Ohms? Suppose the source voltage is 20V. What is the voltage across the capacitor at the specific time above? What is the voltage across the resistor at the specific time above? What is the current i c through the capacitor in the above problem when it is charged to 95%? How long would it take for the capacitor above to charge to 10V? How long would it take for the capacitor to charge to 16V? Suppose the capacitor has been fully charged to 100%, and you replaced the voltage source with a short. How long would it take for the capacitor to fully discharge?

What is the time constant for a 8H coil with 10,000 ohms of series resistance? An 8H inductor and a 10,000Ω resistor connected in series to a 10V source. What is the current through the inductor at 600us? What is the voltage across the inductor at 600us? What is the voltage across the resistor at the specific time above?

1.Find C T 2. Using V C = V S (1 - e -t/  ), what is the voltage across a capacitor at 10 seconds if R = 5Ω, C=2F, and V S = 8V 3. What is the capacitance in Farads of a capacitor that has a vacuum for a dielectric, where the plates are 1mm x 1mm separated by a distance of 1  m. 14F 5.06V 8.85pF

What is  ? How many Tau does it take to get exactly charge a capacitor to 75% of being fully charged? How long does it take to charge a capacitor to fully charged if there is no resistor in the circuit? A capacitor acts like a ___________ under DC conditions and a ____________ under high frequencies. Today we will learn how capacitors and inductors act under normal frequencies open short

A long time constant is defined as one in which the RC time constant (τ) is at least five times longer, in time, than the pulse width of the applied waveform. As a result, the capacitor of a series RC circuit accumulates very little charge, and V C remains small. Draw V C

A medium time constant is defined as one in which the RC time constant (τ), in time, is equal to the pulse width of the applied waveform. As a result, the voltage across the capacitor of a series RC circuit falls between that of a long and short time constant circuit. Draw V C An RC circuit can be used to convert a Square wave signal into a Triangle signal. Also known as an Integrator circuit.

A short time constant is defined as one in which the time constant is no more than one-fifth the pulse width, in time, of the applied voltage. Here, the capacitor quickly charges to the applied voltage and remains there until the input drops to zero. Then the capacitor quickly discharges to zero. Draw V C

Capacitive and Inductive Reactance

Keeping in mind: Inductors act like shorts under DC and opens at instant change. Capacitors act like opens under DC and shorts at instant change. An AC signal is voltage level that is constantly changing. (at a constant rate) Both inductors and capacitors resist this mid level voltage change. (Not 0 Hz but not high freq either). Since Sine waves are continuous, this resistance is constant. In this sense, you can say capacitors are like constant resistors under steady AC waveforms.

The resistance or opposition that inductors and capacitors have towards an AC signal is not called resistance, it is called REACTANCE. Reactance for a capacitor is labeled X C. Reactance for an inductor is labeled X L. If both resistance and reactance exist in a circuit, then this total opposition is called IMPEDANCE: IMPEDANCE - THE TOTAL OPPOSITION TO CURRENT FLOW. Impedance is labeled Z Measured in OHMS! (Units is Ω)

Because the plates of a capacitor are changing polarity at the same rate as the AC voltage, the capacitor seems to pass AC. Suppose you put capacitor in series with your scope probes when you were measuring voltage signal that contained both AC and DC parts. What would your oscope show?

Capacitors have LESS reactance under 2 conditions: (What do you think they are?) 1. Increase in frequency 2. Increase in Capacitance

= 15.9Ω = 39.8kΩ

= 1061 Hz = 3nF

What is the current flowing in the circuit below? However, this is not the whole story. Capacitors don’t act purely like a resistor. Why? There is a lag, as we will see in a few slides.

What would be the total capacitance in this circuit? Total Current?

What is the current flowing in the circuit below? Once you’ve converted Capacitors into resistances, treat them like resistors when doing the math.

Why is X C measured in ohms? What is the proportionality between f and X C ? What is the proportionality between C and X C ?

rubiks cube Below for break

Inductors have MORE reactance under 2 conditions: (What do you think they are?) 1. Increase in frequency 2. Increase in Inductance

= 62.8Ω = 154Ω

= 1432 Hz = 3.2mH

What is the current flowing in the circuit below? However, this is not the whole story. Inductors don’t act purely resistive either. Why? There is a lag, as we will see in a few slides. Can you graph this current

The answer for current in the previous problem was 332mA. This current would look sinusoidal if you graphed it. (Similar to voltage) It is not a flat signal. Would this current be graphed as peak-to-peak? Peak? RMS? Average?

The difference between reactance and resistance is with reactance there is a delay of some sort. Its called reactance because inductors and capacitors react to voltage changes, and it takes time to react, while resistors resist instantly as voltage changes.

Does capacitor current lead or lag capacitor voltage? ICE Current in a capacitor leads voltage in a capacitor By how many degrees?90 degrees

Reactance of an Inductor

Does inductor voltage lead or lag inductor current? ELI Voltage in an inductor leads current in an inductor By how many degrees?90 degrees

ELI the ICEman A pneumonic for remembering the leading and lagging characteristics for inductors and capacitors is:

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