Question Bank: Capacitors |
1
One of the following units is equivalent to the Farad
\[\frac{A^2.S^2 }{kg.m^3}\;\;\;\;\;\;-C\]
\[\frac{A^2.S^3 }{kg.m^2}\;\;\;\;\;\;-A\]
\[\frac{A^2.S^4 }{kg.m^2}\;\;\;\;\;\;-D\]
\[ \frac{A^2.S^2 }{kg.m^3}\;\;\;\;\;\;-B\]
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2
One of the following electrical devices is used to store electric charges and discharge them all at once
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3
A capacitor had a potential difference of
\[12\;V\] across its terminals, acquiring a charge of
\[3\;nC\]. The source voltage was then reduced to
\[7\;V\]
One of the following answers correctly represents the charge and capacitance of the capacitor after the source voltage change.
\[q_2= 2.25×10^{-9}\;\;C\;\;\;\;,\;\;\;\; c=3.2×10^{-10}\;\;F\;\;\;\;\;\;-C\]
\[q_2= 2×10^{-9}\;\;C\;\;\;\;,\;\;\;\; c=2.8×10^{-10}\;\;F\;\;\;\;\;\;-A\]
\[q_2= 4×10^{-9}\;\;C\;\;\;\;,\;\;\;\; c=5.7×10^{-10}\;\;F\;\;\;\;\;\;-D\]
\[ q_2= 1.75×10^{-9}\;\;C\;\;\;\;,\;\;\;\; c=2.5×10^{-10}\;\;F\;\;\;\;\;\;-B\]
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4
A parallel-plate capacitor has a capacitance of
\[6\;nF\]. The shared area between the plates was doubled, and the distance between the plates was halved
while keeping the same insulating material.
The capacitance of the capacitor becomes
\[C=6 \;nF\;\;\;\;\;\;-C\]
\[C=12 \;nF\;\;\;\;\;\;-A\]
\[C=18 \;nF\;\;\;\;\;\;-D\]
\[ C=24 \;nF\;\;\;\;\;\;-B\]
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5
A student studied the factors affecting the capacitance of a parallel-plate capacitor. The distance between the plates was changed while keeping other factors constant. The relationship between the capacitance and the inverse of the distance between the plates was plotted, resulting in the following graph. The common area between the plates equals:
\[A= 6 \;\;Cm^2\;\;\;\;\;\;-C\]
\[A= 2 \;\;Cm^2\;\;\;\;\;\;-A\]
\[A= 9 \;\;Cm^2\;\;\;\;\;\;-D\]
\[ A= 4 \;\;Cm^2\;\;\;\;\;\;-B\]
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6
A student studied the factors affecting the capacitance of a parallel-plate capacitor. The common area between the plates was changed while keeping other factors constant. The relationship between the capacitance and the common area between the plates was plotted, resulting in the following graph. The distance between the plates equals:
\[d= 5.26×10^{−7}\;\;m\;\;\;\;\;\;-C\]
\[d= 9.58×10^{−7} \;\;m\;\;\;\;\;\;-A\]
\[d= 3.41×10^{−7}\;\;m\;\;\;\;\;\;-D\]
\[ d= 1.77×10^{−7}\;\;m\;\;\;\;\;\;-B\]
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7
The Earth is considered a giant spherical capacitor with a radius equal to
( R= 6.38 ×106m )
It possesses a capacitance of
\[C= 6×10^{4}\;\;F\;\;\;\;\;\;-C\]
\[C= 3×10^{4} \;\;F\;\;\;\;\;\;-A\]
\[C= 4×10^{4}\;\;F\;\;\;\;\;\;-D\]
\[ C= 5×10^{4}\;\;F\;\;\;\;\;\;-B\]
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8
A cylindrical capacitor with a length of
\[8\;cm\] is composed of two concentric cylinders with an inner radius of
\[3\;cm\] and an outer radius of
\[6\;cm\]. It is connected to a battery with a potential difference of
\[12\;V\]. The charge on one of the cylinders equals
\[q= 7.7×10^{-11}\;\;c\;\;\;\;\;\;-C\]
\[q= 3.6×10^{-11} \;\;c\;\;\;\;\;\;-A\]
\[q= 2.1×10^{-11}\;\;c\;\;\;\;\;\;-D\]
\[ q= 5.2×10^{-11}\;\;c\;\;\;\;\;\;-B\]
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9
Three capacitors are connected as shown in the figure below. One of the following answers correctly represents the connection method.
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10
Three capacitors are connected as shown in the figure below. One of the following answers correctly represents the connection method.
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11
The total capacitance of a set of capacitors connected as shown in the figure below is:
\[C_{eq}= 6.53 \;\; 𝜇𝐹 \;\;\;\;\;\;-C\]
\[C_{eq}= 3.45 \;\; 𝜇𝐹 \;\;\;\;\;\;-A\]
\[C_{eq}= 12.7 \;\; 𝜇𝐹 \;\;\;\;\;\;-D\]
\[C_{eq}= 8.82 \;\; 𝜇𝐹 \;\;\;\;\;\;-B\]
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12
The total capacitance of a group of capacitors connected as shown in the figure below:
\[C_{eq}= 6 \;\; 𝜇𝐹 \;\;\;\;\;\;-C\]
\[C_{eq}= 8 \;\; 𝜇𝐹 \;\;\;\;\;\;-A\]
\[C_{eq}= 2.7 \;\; 𝜇𝐹 \;\;\;\;\;\;-D\]
\[C_{eq}= 13 \;\; 𝜇𝐹 \;\;\;\;\;\;-B\]
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13
Three capacitors are connected as shown in the figure below with capacitances:
\[C_1=3 µF , C_2= 9 µF , C_3= 18 µF\]
They are connected to a battery with a potential difference of
\[6\;V\]
The charge on the second capacitor is equal to
\[q_2= 0.8×10^{-5}\;\;c\;\;\;\;\;\;-C\]
\[q_2= 3.4×10^{-5} \;\;c\;\;\;\;\;\;-A\]
\[q_2= 2.7×10^{-5}\;\;c\;\;\;\;\;\;-D\]
\[ q_2= 1.2×10^{-5}\;\;c\;\;\;\;\;\;-B\]
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14
Three identical capacitors are connected in four different ways as shown in the figure.
The correct order of their equivalent capacitances from highest to lowest is:
\[C_4>C_2>C_3>C_4\;\;\;\;\;\;-C\]
\[ C_2>C_3>C_1>C_4\;\;\;\;\;\;-A\]
\[C_1>C_3>C_2>C_4\;\;\;\;\;\;-D\]
\[ C_1>C_4>C_3>C_2\;\;\;\;\;\;-B\]
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15
A set of capacitors is connected as shown in the figure below with capacitances:
\[C_1=4 nF , C_2=6 nF , C_3=2 nF \]
and connected to a battery with a potential difference of:
\[∆𝑉=24 V\]
The total energy stored in the set of capacitors is equal to:
\[ U= 6.25× 10^{-6}\;J\;\;\;\;\;\;-C\]
\[ U= 1.32× 10^{-6}\;J\;\;\;\;\;\;-A\]
\[ U= 3.45× 10^{-6}\;J\;\;\;\;\;\;-D\]
\[ U= 8.17× 10^{-6}\;J\;\;\;\;\;\;-B\]
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16
( 16 ) A set of identical capacitors are connected as shown in the figure below and connected to a battery. Each capacitor acquired a charge of:
\[ q= 8 𝜇𝐶 \] The stored energy was calculated to be:
\[U=1× 10^-3\] The capacitance of each capacitor is equal to:
\[C= 8.81×10^{-7}\;\;F\;\;\;\;\;\;-C\]
\[C= 5.12×10^{-7} \;\;F\;\;\;\;\;\;-A\]
\[C= 2.41×10^{-7}\;\;F\;\;\;\;\;\;-D\]
\[ C= 6.85×10^{-7}\;\;F\;\;\;\;\;\;-B\]
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17
Three capacitors with different capacitances are connected as shown in the figure below. One of the following answers matches the connection method:
\[q_2=q_3 \;\;\;\;,\;\;\;\;V_2=V_3 \;\;\;\;\;\;-C\]
\[ q_1=q_2=q_3 \;\;\;\;,\;\;\;\;V_1=V_2=V_3 \;\;\;\;\;\;-A\]
\[q_1=q_2+q_3 \;\;\;\;,\;\;\;\;V=V_1+V_2+V_3 \;\;\;\;\;\;-D\]
\[ q_1=q_2+q_3 \;\;\;\;,\;\;\;\;V=V_1+V_2\;\;\;\;\;\;-B\]
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18
A parallel-plate capacitor connected to a battery has its plate separation doubled while keeping other factors constant. One of the following answers is correct:
Capacitance doubles – Potential remains constant – Charge doubles – Electric field doubles -C
Capacitance halves – Potential remains constant – Charge halves – Electric field halves -A
Capacitance halves – Potential doubles – Charge halves – Electric field remains constant -D
Capacitance remains constant – Potential doubles – Charge doubles – Electric field remains constant -B
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19.
A capacitor is connected to a battery until it is fully charged, then disconnected from the battery. The distance between the plates is doubled while keeping other factors constant. One of the following answers is correct:
Capacitance doubles – Potential remains constant – Charge doubles – Electric field doubles -C
Capacitance halves – Potential remains constant – Charge halves – Electric field halves -A
Capacitance halves – Potential doubles – Charge halves – Electric field remains constant -D
Capacitance remains constant – Potential doubles – Charge doubles – Electric field remains constant -B
Capacitance doubles – Potential remains constant – Charge doubles – Electric field doubles -C
Capacitance remains constant – Potential doubles – Charge doubles – Electric field remains constant -A
Capacitance halves – Potential doubles – Charge remains constant – Electric field remains constant -D
Capacitance halves – Potential remains constant – Charge halves – Electric field halves -B
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20
An air-filled parallel-plate capacitor is connected to a battery. A dielectric material is inserted between the plates. One of the following answers correctly describes the physical changes that occur in the capacitor:
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21
A parallel-plate air capacitor is connected to a battery. After being disconnected from the battery, a dielectric material is inserted between the plates. Which of the following answers correctly describes the physical changes that occur to the capacitor?
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22
A parallel-plate air capacitor has a capacitance
\[C=5\;nF\]. The length of each plate is
\[ 2L\], its width is
\[L\], and the distance between the plates is
\[d\]. A dielectric material with a dielectric constant
\[K=5\] is inserted between the plates, with a length of
\[0.5L\], a width of
\[L\], and a height equal to the distance between the plates, as shown in the figure below.
The new capacitance of the capacitor becomes:
\[C= 10 \;\; n𝐹 \;\;\;\;\;\;-C\]
\[C= 25 \;\; n𝐹 \;\;\;\;\;\;-A\]
\[C= 15 \;\; n𝐹 \;\;\;\;\;\;-D\]
\[C= 20 \;\; n𝐹 \;\;\;\;\;\;-B\]
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One of the following units is equivalent to the Farad
\[\frac{A^2.S^2 }{kg.m^3}\;\;\;\;\;\;-C\] |
\[\frac{A^2.S^3 }{kg.m^2}\;\;\;\;\;\;-A\] |
\[\frac{A^2.S^4 }{kg.m^2}\;\;\;\;\;\;-D\] |
\[ \frac{A^2.S^2 }{kg.m^3}\;\;\;\;\;\;-B\] |
One of the following electrical devices is used to store electric charges and discharge them all at once
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A capacitor had a potential difference of \[12\;V\] across its terminals, acquiring a charge of \[3\;nC\]. The source voltage was then reduced to \[7\;V\] One of the following answers correctly represents the charge and capacitance of the capacitor after the source voltage change.
\[q_2= 2.25×10^{-9}\;\;C\;\;\;\;,\;\;\;\; c=3.2×10^{-10}\;\;F\;\;\;\;\;\;-C\] |
\[q_2= 2×10^{-9}\;\;C\;\;\;\;,\;\;\;\; c=2.8×10^{-10}\;\;F\;\;\;\;\;\;-A\] |
\[q_2= 4×10^{-9}\;\;C\;\;\;\;,\;\;\;\; c=5.7×10^{-10}\;\;F\;\;\;\;\;\;-D\] |
\[ q_2= 1.75×10^{-9}\;\;C\;\;\;\;,\;\;\;\; c=2.5×10^{-10}\;\;F\;\;\;\;\;\;-B\] |
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The capacitance of the capacitor becomes
\[C=6 \;nF\;\;\;\;\;\;-C\] |
\[C=12 \;nF\;\;\;\;\;\;-A\] |
\[C=18 \;nF\;\;\;\;\;\;-D\] |
\[ C=24 \;nF\;\;\;\;\;\;-B\] |
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A student studied the factors affecting the capacitance of a parallel-plate capacitor. The distance between the plates was changed while keeping other factors constant. The relationship between the capacitance and the inverse of the distance between the plates was plotted, resulting in the following graph. The common area between the plates equals:
\[A= 6 \;\;Cm^2\;\;\;\;\;\;-C\] |
\[A= 2 \;\;Cm^2\;\;\;\;\;\;-A\] |
\[A= 9 \;\;Cm^2\;\;\;\;\;\;-D\] |
\[ A= 4 \;\;Cm^2\;\;\;\;\;\;-B\] |
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A student studied the factors affecting the capacitance of a parallel-plate capacitor. The common area between the plates was changed while keeping other factors constant. The relationship between the capacitance and the common area between the plates was plotted, resulting in the following graph. The distance between the plates equals:
\[d= 5.26×10^{−7}\;\;m\;\;\;\;\;\;-C\] |
\[d= 9.58×10^{−7} \;\;m\;\;\;\;\;\;-A\] |
\[d= 3.41×10^{−7}\;\;m\;\;\;\;\;\;-D\] |
\[ d= 1.77×10^{−7}\;\;m\;\;\;\;\;\;-B\] |
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The Earth is considered a giant spherical capacitor with a radius equal to
( R= 6.38 ×106m )
It possesses a capacitance of
\[C= 6×10^{4}\;\;F\;\;\;\;\;\;-C\] |
\[C= 3×10^{4} \;\;F\;\;\;\;\;\;-A\] |
\[C= 4×10^{4}\;\;F\;\;\;\;\;\;-D\] |
\[ C= 5×10^{4}\;\;F\;\;\;\;\;\;-B\] |
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A cylindrical capacitor with a length of
\[8\;cm\] is composed of two concentric cylinders with an inner radius of
\[3\;cm\] and an outer radius of
\[6\;cm\]. It is connected to a battery with a potential difference of
\[12\;V\]. The charge on one of the cylinders equals
\[q= 7.7×10^{-11}\;\;c\;\;\;\;\;\;-C\] |
\[q= 3.6×10^{-11} \;\;c\;\;\;\;\;\;-A\] |
\[q= 2.1×10^{-11}\;\;c\;\;\;\;\;\;-D\] |
\[ q= 5.2×10^{-11}\;\;c\;\;\;\;\;\;-B\] |
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Three capacitors are connected as shown in the figure below. One of the following answers correctly represents the connection method.
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Three capacitors are connected as shown in the figure below. One of the following answers correctly represents the connection method.
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The total capacitance of a set of capacitors connected as shown in the figure below is:
\[C_{eq}= 6.53 \;\; 𝜇𝐹 \;\;\;\;\;\;-C\] |
\[C_{eq}= 3.45 \;\; 𝜇𝐹 \;\;\;\;\;\;-A\] |
\[C_{eq}= 12.7 \;\; 𝜇𝐹 \;\;\;\;\;\;-D\] |
\[C_{eq}= 8.82 \;\; 𝜇𝐹 \;\;\;\;\;\;-B\] |
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The total capacitance of a group of capacitors connected as shown in the figure below:
\[C_{eq}= 6 \;\; 𝜇𝐹 \;\;\;\;\;\;-C\] |
\[C_{eq}= 8 \;\; 𝜇𝐹 \;\;\;\;\;\;-A\] |
\[C_{eq}= 2.7 \;\; 𝜇𝐹 \;\;\;\;\;\;-D\] |
\[C_{eq}= 13 \;\; 𝜇𝐹 \;\;\;\;\;\;-B\] |
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Three capacitors are connected as shown in the figure below with capacitances:
\[C_1=3 µF , C_2= 9 µF , C_3= 18 µF\]
They are connected to a battery with a potential difference of
\[6\;V\]
The charge on the second capacitor is equal to
\[q_2= 0.8×10^{-5}\;\;c\;\;\;\;\;\;-C\] |
\[q_2= 3.4×10^{-5} \;\;c\;\;\;\;\;\;-A\] |
\[q_2= 2.7×10^{-5}\;\;c\;\;\;\;\;\;-D\] |
\[ q_2= 1.2×10^{-5}\;\;c\;\;\;\;\;\;-B\] |
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Three identical capacitors are connected in four different ways as shown in the figure.
The correct order of their equivalent capacitances from highest to lowest is:
\[C_4>C_2>C_3>C_4\;\;\;\;\;\;-C\] |
\[ C_2>C_3>C_1>C_4\;\;\;\;\;\;-A\] |
\[C_1>C_3>C_2>C_4\;\;\;\;\;\;-D\] |
\[ C_1>C_4>C_3>C_2\;\;\;\;\;\;-B\] |
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A set of capacitors is connected as shown in the figure below with capacitances: \[C_1=4 nF , C_2=6 nF , C_3=2 nF \] and connected to a battery with a potential difference of: \[∆𝑉=24 V\] The total energy stored in the set of capacitors is equal to:
\[ U= 6.25× 10^{-6}\;J\;\;\;\;\;\;-C\] |
\[ U= 1.32× 10^{-6}\;J\;\;\;\;\;\;-A\] |
\[ U= 3.45× 10^{-6}\;J\;\;\;\;\;\;-D\] |
\[ U= 8.17× 10^{-6}\;J\;\;\;\;\;\;-B\] |
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( 16 ) A set of identical capacitors are connected as shown in the figure below and connected to a battery. Each capacitor acquired a charge of:
\[ q= 8 𝜇𝐶 \] The stored energy was calculated to be:
\[U=1× 10^-3\] The capacitance of each capacitor is equal to:
\[C= 8.81×10^{-7}\;\;F\;\;\;\;\;\;-C\] |
\[C= 5.12×10^{-7} \;\;F\;\;\;\;\;\;-A\] |
\[C= 2.41×10^{-7}\;\;F\;\;\;\;\;\;-D\] |
\[ C= 6.85×10^{-7}\;\;F\;\;\;\;\;\;-B\] |
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Three capacitors with different capacitances are connected as shown in the figure below. One of the following answers matches the connection method:
\[q_2=q_3 \;\;\;\;,\;\;\;\;V_2=V_3 \;\;\;\;\;\;-C\] |
\[ q_1=q_2=q_3 \;\;\;\;,\;\;\;\;V_1=V_2=V_3 \;\;\;\;\;\;-A\] |
\[q_1=q_2+q_3 \;\;\;\;,\;\;\;\;V=V_1+V_2+V_3 \;\;\;\;\;\;-D\] |
\[ q_1=q_2+q_3 \;\;\;\;,\;\;\;\;V=V_1+V_2\;\;\;\;\;\;-B\] |
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A parallel-plate capacitor connected to a battery has its plate separation doubled while keeping other factors constant. One of the following answers is correct:
Capacitance doubles – Potential remains constant – Charge doubles – Electric field doubles -C |
Capacitance halves – Potential remains constant – Charge halves – Electric field halves -A |
Capacitance halves – Potential doubles – Charge halves – Electric field remains constant -D |
Capacitance remains constant – Potential doubles – Charge doubles – Electric field remains constant -B |
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A capacitor is connected to a battery until it is fully charged, then disconnected from the battery. The distance between the plates is doubled while keeping other factors constant. One of the following answers is correct:
Capacitance doubles – Potential remains constant – Charge doubles – Electric field doubles -C |
Capacitance halves – Potential remains constant – Charge halves – Electric field halves -A |
Capacitance halves – Potential doubles – Charge halves – Electric field remains constant -D |
Capacitance remains constant – Potential doubles – Charge doubles – Electric field remains constant -B |
Capacitance doubles – Potential remains constant – Charge doubles – Electric field doubles -C |
Capacitance remains constant – Potential doubles – Charge doubles – Electric field remains constant -A |
Capacitance halves – Potential doubles – Charge remains constant – Electric field remains constant -D |
Capacitance halves – Potential remains constant – Charge halves – Electric field halves -B |
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An air-filled parallel-plate capacitor is connected to a battery. A dielectric material is inserted between the plates. One of the following answers correctly describes the physical changes that occur in the capacitor:
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A parallel-plate air capacitor is connected to a battery. After being disconnected from the battery, a dielectric material is inserted between the plates. Which of the following answers correctly describes the physical changes that occur to the capacitor?
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A parallel-plate air capacitor has a capacitance
\[C=5\;nF\]. The length of each plate is
\[ 2L\], its width is
\[L\], and the distance between the plates is
\[d\]. A dielectric material with a dielectric constant
\[K=5\] is inserted between the plates, with a length of
\[0.5L\], a width of
\[L\], and a height equal to the distance between the plates, as shown in the figure below.
The new capacitance of the capacitor becomes:
\[C= 10 \;\; n𝐹 \;\;\;\;\;\;-C\] |
\[C= 25 \;\; n𝐹 \;\;\;\;\;\;-A\] |
\[C= 15 \;\; n𝐹 \;\;\;\;\;\;-D\] |
\[C= 20 \;\; n𝐹 \;\;\;\;\;\;-B\] |
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