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23.10 RL Circuits
The energy is given by the equation and all quantities are known.
If the current is suddenly switched off, this amount of energy is enough to cause a spark.
Unless the power input is infinite, it cannot be built up quickly.
The current through an inductor can't be turned on or off instantly.
An emf opposing the change is caused by the change in current changes.
A current is established when the battery, resistors, and inductor are in series.
The current stops when the battery is removed in position 2.
The current is zero when the switch is first moved to position 1 and eventually rises to where the total resistance of the circuit is.
The amount of change is the most important factor in determining the opposition of the inductor.
As the current approaches its final value, an emf decreases to zero, which is the opposition it poses.
The amount of change left is proportional to the opposing emf.
There is a similarity between the exponential behavior of the voltage on a chargingCapacitor and the current in an RL circuit.
In the next time, the current will go 0.632 The property of the exponential is that the final value is never exactly reached, but 0.632 of the remaining value is achieved in every characteristic time.
The final value is almost achieved in just a few multiples of the time.
The time is dependent on two factors, inductance and resistance.
It makes sense since a large inductance is very effective in opposing change.
The bigger the resistance, the greater it is.
This makes sense since a large final current and change is what it takes to get there.
More energy is stored in the inductor and more time is required to get it out.
Since the inductor is opposed to the decrease in current by inducing an emf in the same direction as the battery that drove the current, this is not instantaneous.
The amount of energy stored in the inductor is dissipated at a finite rate.
The rate of decrease slows as the current approaches zero.
In the first few days after the switch is closed, the current falls to its initial value.
The time constant is determined by.
This is not a long time.
The coil will be close to its full current in about ten time constants.
The current can be found by either using or considering the decline in steps.
The process in steps is considered since the time is twice the characteristic time.
After another 2.50 ms, or a total of 5.00 ms, the current falls to 0.368 of the value found.
We look at how an RL circuit behaves when an AC voltage is applied.
Capacitors and inductors are included in many circuits.
Capacitors and inductors respond to DC voltages when they are switched on and off.
Inductors and Capacitors react to AC voltages.
Since we can make the resistance of an inductor so small that it has a negligible effect on the circuit, it is reasonable to assume negligible resistance.
The graph of voltage and current are functions of time.
When DC voltage was switched on in the preceding section, the current started at zero and rose to its peak after the voltage that drives it.
At point a, the current begins to decrease; at point b, it becomes zero.
Following the voltage, the current becomes negative.
At point c the current becomes less negative.
The current goes through zero at point d when the voltage reaches its positive peak.
Inductors oppose change in current.
Changing current causes a back emf.
This is an effective resistance of the inductor.
An analysis of the circuit using the loop rule and calculus actually produces this expression.
It makes sense that the greater the resistance to change, the more it is proportional to.
It's reasonable that the change in current is proportional to the Frequency.
That is large frequencies for small ones.
The expression is where the reactance is found.
Ohm's law can be used to find the current at each Frequency.
The inductor reacts differently at different frequencies.
The reactance is large and the current is small, consistent with how an inductor impedes rapid change.
High frequencies are interfered with the most.
A large inductor can be put in series with a sound reproduction system to reduce high-frequency sound output from your speakers or high-frequency power spikes into your computer.
The resistance in the circuit is negligible, but the AC current is not very large because of the reactance.
There is no time for the current to get large with AC.
We can assume negligible resistance because the resistance of this circuit can be made so small.
The function of time in the figure is graphed as a function of voltage and current.
The current is zero because theCapacitor is fully charged and stops the flow.
At point a, theCapacitor has fully discharged and the voltage across it is zero.
The negative current between points a and b causes the voltage on theCapacitor to reverse.
The current is zero and the voltage is negative at point b.
The current can reach its maximum when the charge on theCapacitor is zero and the voltage is zero at point b.
The current goes to zero between points c and d as the voltage goes to its peak.
The ability to stop the current when fully charged is what the Capacitor is affecting.
The rms current is limited by the Capacitor since an AC voltage is applied.
The less time there is to fully charge the capacitor, the less current there is.
The expression in is where the reactance is found.
The inductor reacts in exactly the same way as the capacitor does at the two different frequencies.
The current is large and the reactance is small.
Capacitors favor change while inductors oppose it.
Capacitors impede low frequencies the most since they have less time to stop the current.
Capacitors can be used to remove low frequencies.
A sound reproduction system rids aCapacitor in series of the hum.
There is an rms current in a circuit with an AC voltage applied to a capacitor.
The voltage is reversing, charging and discharging.
The current is zero if the Frequency goes to zero.
The reactance of theCapacitor is very low at high frequencies, it acts like a simple wire and does not impede the current.
Capacitors have a different effect on AC circuits than inductors.
Figure 23.47 shows an AC voltage applied to a Resistor and a graph of voltage and current versus time.
The current and voltage are in the same place.
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