Case Study 1: Electrostatic Potential Due to a Point Charge
The electrostatic potential V
due to a point charge Q at a distance rrr from the charge is given by the
formula:
\(\ V = \frac{kQ}{r} \)
where k is Coulomb's
constant. The electrostatic potential is a scalar quantity and depends on the
position of the point charge. It is positive for a positive charge and negative
for a negative charge.
Questions:
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The electrostatic potential V is:
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a) A vector quantity
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b) A scalar quantity
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c) Zero everywhere
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d) Dependent on the medium
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If the distance from the point charge is halved, the
potential at that point will:
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a) Double
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b) Halve
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c) Quadruple
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d) Remain the same
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What happens to the potential due to a negative charge
as the distance increases?
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a) It increases
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b) It decreases
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c) It remains constant
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d) It becomes zero
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The unit of electrostatic potential is:
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a) Coulomb
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b) Joule
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c) Volt
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d) Farad
Answers:
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b) A scalar quantity
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c) Quadruple
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b) It decreases
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c) Volt
Case Study 2: Work Done in Moving a Charge in an Electric Field
When a charge q is moved from
point A to point B in an electric field, work W is done by the electric field.
The work done is related to the electrostatic potential difference \(\Delta V \)
between the two points:
\(\ W= \Delta V \)
If the electric field is
uniform, the work done can also be expressed as:
\(\ W = F \cdot d \cdot \cos \theta \)⋅⋅
where F is the force, d is
the distance moved, and \(\ \theta \) is the angle between the force and the
displacement.
Questions:
-
The work done in moving a charge in an electric field
is dependent on:
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a) The charge only
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b) The distance only
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c) The potential difference
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d) All of the above
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If a positive charge moves against the electric field,
the work done is:
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a) Positive
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b) Negative
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c) Zero
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d) Undefined
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When moving a charge in a uniform electric field, if
the angle \(\ \theta\) is
\(\ 90^\circ \) , the work done is:
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a) Maximum
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b) Minimum
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c) Zero
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d) Infinite
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The electrostatic potential energy of a charge in an
electric field is:
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a) Directly proportional to the charge and the potential
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b) Inversely proportional to the distance
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c) Independent of the field strength
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d) Always negative
Answers:
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c) The potential difference
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a) Positive
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c) Zero
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a) Directly proportional to the charge and the
potential
Case Study 3: Capacitance and Capacitors
A capacitor is a device used to
store electric charge. The capacitance C of a capacitor is defined as the
ratio of the charge Q stored on one plate to the potential difference V
across the plates:
\(\ C= \frac{Q}{V}\)
Capacitance is measured in
farads (F) and depends on the physical characteristics of the capacitor, such as
the area of the plates, the distance between them, and the dielectric material
used.
Questions:
-
The capacitance of a capacitor depends on:
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a) The area of the plates
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b) The distance between the plates
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c) The dielectric material
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d) All of the above
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If the area of the plates of a capacitor is doubled
while keeping the distance constant, the capacitance will:
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a) Double
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b) Halve
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c) Quadruple
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d) Remain the same
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A capacitor stores energy given by the formula:
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a) \(\frac{1}{2} CV^{2}\)
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b) CV
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c) QV
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d) \(\frac{1}{2} QV\)
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What effect does inserting a dielectric material
between the plates of a capacitor have?
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a) Increases the capacitance
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b) Decreases the capacitance
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c) No effect on capacitance
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d) Changes the charge on the plates
Answers:
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d) All of the above
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a) Double
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a) \(\frac{1}{2} CV^{2}\)
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a) Increases the capacitance
Case Study 4: Energy Stored in a Capacitor
When a capacitor is charged,
work is done to move charge against the electric field. The energy stored in a
capacitor can be calculated using the formula:
\(\ U= \frac{1}{2}
CV^{2}\)
where U is the stored energy,
C is the capacitance, and VVV is the potential difference across the
capacitor.
Questions:
-
The energy stored in a capacitor is directly
proportional to:
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a) The charge alone
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b) The potential difference alone
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c) The capacitance alone
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d) The square of the potential difference
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If the voltage across a capacitor is tripled, the
energy stored in the capacitor will increase by a factor of:
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In a series circuit, the total capacitance is:
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a) Greater than the smallest capacitance
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b) The sum of individual capacitances
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c) Less than the smallest capacitance
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d) The average of individual capacitances
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In a parallel circuit, the total capacitance is:
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a) The sum of the reciprocals of individual capacitances
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b) The product of individual capacitances
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c) Greater than the largest capacitance
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d) The sum of individual capacitances
Answers:
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d) The square of the potential difference
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c) 9
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c) Less than the smallest capacitance
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d) The sum of individual capacitances
Case Study 5: Applications of Capacitors
Capacitors are widely used in
electronic circuits for various applications such as filtering, timing, and
energy storage. In audio equipment, capacitors can smooth out signals and reduce
noise. In power supply circuits, they can store energy and release it when
needed to maintain a stable voltage.
Questions:
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Which of the following is a common application of
capacitors?
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a) Amplifying signals
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b) Filtering noise
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c) Storing energy
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d) All of the above
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In timing circuits, capacitors are used in conjunction
with:
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a) Resistors
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b) Inductors
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c) Diodes
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d) Transistors
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In power supply circuits, capacitors help to:
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a) Increase voltage
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b) Stabilize voltage
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c) Decrease current
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d) Reduce resistance
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What happens to the energy stored in a capacitor when
it is discharged?
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a) It is converted to heat
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b) It is dissipated as sound
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c) It is released as electrical energy
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d) It remains in the capacitor
Answers:
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d) All of the above
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a) Resistors
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b) Stabilize voltage
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c) It is released as electrical energy