PLEASE ANSWER THIS QUESTION AS SOON AS POSSIBLE
PLEASE ANSWER THIS QUESTION AS SOON AS POSSIBLE 6. Deduce the expression the the parallel combination Consider the following elec 20101 ent resistance of tors R t. R2 and R circuit : (a) Which two resistors are ccnnected in series ? (b) Which two resistors connected in parallel ? (c) If every resjstor oi the circuit is of 2 Q, what current Will now in the cjrcujt ? (HOT S, Foreign 2010)
Answers
In radio engineering and in other branches of
electrotechnology it is the practice to give circuits
specified frequency-dependent characteristics by
using capacitors and coils. These two circuit elements have properties that are to a certain extent
opposed to one another. When an alternating voltage is applied, the current flowing in a capacitor
leads the voltage in phase, whereas in a coil the
current lags in phase. Again, in a capacitor the reactance decreases with rising frequency, whereas
in a coil it increases.
Among the passive electric networks composed of
combinations of capacitors and coils, the electric
filters, which are used for separating signals with
certain frequencies from signals with other frequencies, form an important subgroup. For this purpose
the use of capacitors and coils is not strictly necessary. A filter can be built using only one of these
elements in combination with resistors. By combining coils and capacitors, however, it is easy to produce a much sharper separation between wanted and
unwanted signals.
One of the simplest and most familiar passive filter
networks is the parallel resonant circuit (here referred to as an LC circuit) which can be considered
as formed from the parallel arrangement of a capacitor, a coil (both loss-free) and a resistor (seefig·l).
In such a circuit the modulus of the impedance is
maximum at the resonant frequency
Wo = 1/VLc.
For any given value t» of the frequency, the impedance can be written in the form:
R
Z(w) = -1 -+-j{3-Q'
If Iw - wol is small compared with wo, we can write
{3 in the form:
(3 = 2(w - wo) .
Wo
In this case, then, (3 is twice the "relative detuning" .
In equation (2) Q is the figure' of merit, here given
by:
R
Q=- =woCR.
woL
The modulus of the impedance Z, plotted as a
function of frequency, has the form of the familiar
resonance curve (fig. I). The curve is narrower, i.e.
the LC circuit more selective, the higher the value
of Q. The difference between the two frequencies at
which IZIis a factor of i2 smaller than the maximum
value is normally referred to as the bandwidth.
(3)
IZI
t
-co
(1) Fig. 1.Left:resonantcircuitconsistingof a coil,aninductance,
a capacitanceand a resistancein parallel LC circuit. Right:
frequencycharacteristic(resonancecurve)fortwoLe circuits.
Theresonantfrequencyiswo' Thenetworktowhichcurvea relates has a higherfigureofmerit Q.
(2)
Filters for very low frequencies
1963/64, No. 11/12 ACTIVE FILTERS FOR LOW FREQUENCIES 331
measurements are frequently carried out with intermittent light; examples are measurements of photoconductivity and of light adsorption in liquids and
crystals. The periodic interruption of the light makes
it possible to use AC amplifiers for this purpose,
which are easier to build and to operate than DC
amplifiers. Measurements at very low frequencies
are also important in various electro-medical applications, particularly in cardiography, encephalography and myography.