which is the impedance of an
RLC series AC circuit. For circuits without a resistor, take
; for those without an inductor, take
; and for those without a capacitor, take
.
Calculating impedance and current
An
RLC series circuit has a
resistor, a 3.00 mH inductor, and a
capacitor. (a) Find the circuit’s impedance at 60.0 Hz and 10.0 kHz, noting that these frequencies and the values for
and
are the same as in
[link] and
[link] . (b) If the voltage source has
, what is
at each frequency?
Strategy
For each frequency, we use
to find the impedance and then Ohm’s law to find current. We can take advantage of the results of the previous two examples rather than calculate the reactances again.
Solution for (a)
At 60.0 Hz, the values of the reactances were found in
[link] to be
and in
[link] to be
. Entering these and the given
for resistance into
yields
Similarly, at 10.0 kHz,
and
, so that
Discussion for (a)
In both cases, the result is nearly the same as the largest value, and the impedance is definitely not the sum of the individual values. It is clear that
dominates at high frequency and
dominates at low frequency.
Solution for (b)
The current
can be found using the AC version of Ohm’s law in Equation
:
at 60.0 Hz
Finally, at 10.0 kHz, we find
at 10.0 kHz
Discussion for (a)
The current at 60.0 Hz is the same (to three digits) as found for the capacitor alone in
[link] . The capacitor dominates at low frequency. The current at 10.0 kHz is only slightly different from that found for the inductor alone in
[link] . The inductor dominates at high frequency.
How does an
RLC circuit behave as a function of the frequency of the driving voltage source? Combining Ohm’s law,
, and the expression for impedance
from
gives
The reactances vary with frequency, with
large at high frequencies and
large at low frequencies, as we have seen in three previous examples. At some intermediate frequency
, the reactances will be equal and cancel, giving
—this is a minimum value for impedance, and a maximum value for
results. We can get an expression for
by taking
Substituting the definitions of
and
,
Solving this expression for
yields
where
is the
resonant frequency of an
RLC series circuit. This is also the
natural frequency at which the circuit would oscillate if not driven by the voltage source. At
, the effects of the inductor and capacitor cancel, so that
, and
is a maximum.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.