A parallel-plate capacitor is used as a vibration sensor. The plates have an area of 100cm 2 , the dielectric is air, and the distance between the plates is a function of time given by d ( t ) = 1 + 0.01 sin ( 200 t ) m m A constant voltage of 200 V is applied to the sensor Determine the current through the sensor as a function of time by using the approximation 1 / ( 1 + x ) ≅ 1 − x for x < < 1 . (The argument of the sinusoid is in radians.)
A parallel-plate capacitor is used as a vibration sensor. The plates have an area of 100cm 2 , the dielectric is air, and the distance between the plates is a function of time given by d ( t ) = 1 + 0.01 sin ( 200 t ) m m A constant voltage of 200 V is applied to the sensor Determine the current through the sensor as a function of time by using the approximation 1 / ( 1 + x ) ≅ 1 − x for x < < 1 . (The argument of the sinusoid is in radians.)
Solution Summary: The author calculates the capacitance of a parallel-plate capacitor used as an vibration sensor. The current through the capacitor in terms of time is given by I=(-epsilon _0
A parallel-plate capacitor is used as a vibration sensor. The plates have an area of
100cm
2
, the dielectric is air, and the distance between the plates is a function of time given by
d
(
t
)
=
1
+
0.01
sin
(
200
t
)
m
m
A constant voltage of 200 V is applied to the sensor Determine the current through the sensor as a function of time by using the approximation
1
/
(
1
+
x
)
≅
1
−
x
for
x
<
<
1
. (The argument of the sinusoid is in radians.)
Design a full-wave rectifier power supply using a 9.52:1 transformer. Assume that the outlet is120 V rms @ 60 Hz. Further assume that the diode turn-on voltage V D(on) is 0.7 V. Pick the valueof CL such that vo has a maximum ripple of 1 V p-p . Solve for the average value of vo = Vo (notethat this may be greater than 12 V) and iD(ave) = ID.
Light-emitting diodes (LEDs) are diodes made with III-V compound semiconductor materials such as aluminum gallium arsenide (AlGaAs), aluminum indium gallium phosphide (AlInGaP) or indium gallium nitride (InGaN), instead of silicon. The LEDs emit light when the device is operated under forward bias. LEDs of different colors have different turn-on voltages VD(on). For example:
VD(on) :
Red: ~ 1.6 V
Yellow: ~ 1.7 V
Green: ~ 1.8 V
Blue: ~ 2.8 V
White: ~ 3.8 V
(a) Model these five LEDs with a simplified piecewise linear model
(b) A rule of thumb is that it takes about 1 mA of current to “light” an LED while ~ 10 mA is needed for it to appear bright. Use the piecewise linear model for the LEDs, for the over-voltage indicator circuit to the right, find the values of Vin which will cause D1 or D2 to light (i.e. when ID1 or ID2 exceeds 1 mA).
Consider a fixed and updated instrumentation amplifier (where two resistors are lumped into one
resistor), analyze the circuit if a common voltage source (VICM) is connected to two inputs.
A₁
R₂
+
R₁
R₂,
RA
www
www
R₁
R₁
www
A3
X
R₁
R₂
www
www
R₁₂
+
Vo
RA
A2
V2 O-
+
R₂
12
R₁
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