2
1) For a n-stage cascade circuit, why can’t we reach 2nVmax at the output when the
circuit is loaded?
Answer:
When H.V. output is loaded, I > 0. If the generator supplies any load current I, the output
voltage will never reach the value 2nVmax. There will also be a ripple on the voltage, and
therefore we have to deal with two quantities: the voltage drop ΔV0 and the peak-to-peak
ripple 2δV.
Fig.01. Loaded cascade circuit, definitions of voltage drop ΔV0 and ripple δV
For a given number of stages, a given frequency and capacitance of each stage, the output
voltage decrease linearly with load current I. For a given load, however, V 0= (V0max– V) may
rise initially with the number of stages n, and reaches a maximum value but decays beyond
on optimum number of stage.
3
Where, C’n = C’n-1= …… C’1 = C
V 
n n  1  I  n n  1
I

2 fC
2
4 fC
Voltage drop, ΔV is the difference between the theoretical no load voltage 2nVmax and the
on-load voltage,
V 
I  2 3 n2 n 
 n   
fC  3
2 6
So, the mean output voltage of n-stage cascade circuit is
=2nVmax-ΔV-δV
2) Propose a solution to reduce the voltage drop in a n-stage cascade circuit.
Answer:
For tall constructions in the MV range, the circuit does not comprise all circuit elements
which are influencing the real working conditions. There are not only the impedances of the
diodes and the supply transformer which have to be taken into consideration; stray
capacitances between the two capacitor columns and capacitor elements to ground form a
much more complex network. There are also improved circuits available by adding one or
two additional ‘oscillating’ columns which charge the same smoothing stack. This additional
column can be fed by phase-shifted a.c. voltages, by which the ripple and voltage drop can
further be reduced.
3) Describe very briefly the operation of a Van de Graaff generator with schematic.
Answer:
A Van de Graaff generator pulls electrons from the Earth, moves them along a belt and stores
them on the large sphere. These electrons repel each other and try to get as far away from
each other as possible, spreading out on the surface of the sphere. The Earth has lots of room
for electrons to spread out upon, so electrons will take any available path back to the ground.
The grounding rod is a smaller sphere, attached by a wire to the Earth. It provides a
convenient path for electrons to move to the ground. If we bring the grounding rod close
4
enough to the large sphere, the electrons rip through the air molecules in order to jump onto
the grounding rod, creating a spark and crackling noise.
Fig.02. Schematic diagram of Van de Graaff generator
When a fluorescent light tube approaches the negatively charged generator, the electrons on
the generator flow through the tube and the person holding it. Flowing electrons result in an
electrical current, lighting up the light tube. It doesn't take very much current to light a
fluorescent bulb!
Putting Styrofoam peanuts or confetti on top of the Van de Graaff generator can create a cool
trick. The electrons that collect on the sphere spread out into the Styrofoam peanuts and
confetti, making the little, light objects negatively charged. When the negative charges on the
peanuts repel the negative charges on the generator, the peanuts push off the sphere.
When a student puts a hand on the sphere, the electrons will spread out onto that person as
they repel from the other electrons. They are most obvious in a person's hair because the like
5
charges of the electrons repel each other and cause the hairs to stand up and spread away
from each other. As long as the person is standing on an insulated platform, the electrons will
not be able to travel down to the ground and their hair will remain standing up.
4) Based on the triboelectric series provided in the previous slide, what would happen if:
(a) Lower roller material = silicon, upper roller material = Teflon and belt material =
cotton (b) Lower roller material = Teflon, upper roller material = glass, belt material =
cotton ?
Answer:
The combination of the Teflon roller and the Glass roller would generate a larger static field
than would the Silicon roller and Teflon roller set. This result is consistent with the ranking
of the materials on the triboelectric series chart, whereby Glass is farther away from Teflon
than is Silicon.
5) While operating the Van de Graaff generator at your lab, you observe that voltage is
not being built up to the desired level. What might be some possible reasons behind
this?
Answer:
Several reasons can be responsible for voltage not being built up to the desired level. Such as
Dome size not being large enough,

Rough surface of the ball,

Material selection not based on triboelectric series,

Excessive humidity in air,

Uneven sharpness of upper and lower brush.
6) What would happen if you operate your Van de Graaff generator on a rainy day?
Answer:
A Van de Graaff generator does not function properly on a rainy day. Because the water
vapor in the air carries the charge away. Dry air is pretty decent insulator - but the more water
vapor that is present, the greater the conductivity - and decreasing charge the Van de Graaff
generator can store. Basically the generator is part of a capacitor. One plate is the sphere at
6
the top of the generator, the other is whatever the base is standing on. The ability for a
capacitor to store a charge depends on how well the insulation is between the two plates.
The more humidity - the greater the leak, and the lower the charge.
7) For building up higher potential, should you use a larger or smaller dome? Give
reasons for your answer.
Answer:
The dome should be large enough for building up high potential. Because the larger the
dome, the larger the radius. So, curvature will decrease. As a result, similar charges can
maintain maximum distance. Besides there will be no unwanted discharge as field lines
remains far away from each other. Since charge-storage increases due to larger dome, higher
potential can build up.
8) Mention some methods to increase the voltage that’s built up on dome.
Answer:
Some methods to increase the voltage that’s built up on dome are
Using larger size of dome,

Reducing leakage of electric charges,

Supplying large amount of charges of greater frequency.
9) When you stand on a plastic chair or some proper insulating object and touch the
running Van de Graff generator, your hair stands up. Why?
Answer:
When the Van de Graaff generator starts charging, it transfers the charge to the person who is
touching it. Since the person's hair follicles are getting charged to the same potential, they try
to repel each other. This is why the hair actually stands up. It would not make a difference if
the polarity of the Van de Graaff generator were reversed. As long as the person is insulated,
the charge will build up (assuming, of course, that the hair is clean and dry).
7
10) When you walk on a floor mat on a dry day and touch the metal door knob
afterwards, you might get a shock. Can you relate it to any of the mechanisms discussed
in today’s class? If so, explain briefly.
Answer:
Yes, it can be related to the mechanism (Triboelectric effect) discussed in our respective
class.
When I walk on a floor mat on a dry day, the mat (Specially nylon mat, which is in upper
position in triboelectric series) will give up electrons and generate static electricity. The
charge will induce static electrical charge on my body. So, when I touch the conductive metal
door knob afterwards, the electrons will jump from my body to the knob as well as the static
will discharge and I might get a shock. On a dry day, the air is drier, and it’s easier to build
up electrons on the skin surface. So, the tendency of getting shock will be more.