Charging and Discharging of a Capacitor Through a Resistance and RC Circuits

Q 1 :
The electric field between the two parallel plates of a capacitor of 1.5 $μ F$ capacitance drops to one third of its initial value in 6.6 $μ s$ when the plates are connected by a thin wire.

The resistance of this wire is __________ $Ω .$ (Given, log 3 = 1.1) [2024]

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(4) $E = \frac{Q}{A ϵ_{0}} \Rightarrow E \propto Q \Rightarrow E = E_{0} e^{- t / R C}$

$\Rightarrow t = R C \ln \frac{E_{0}}{E} \Rightarrow 6.6 \times 10^{- 6} = R (1.5 \times 10^{- 6}) \ln 3$

$\Rightarrow R = \frac{66}{151 \ln 3} = \frac{66}{15 \times 1.1} = 4 Ω$

Q 2 :
The charge accumulated on the capacitor connected in the following circuit is ___________ $μ C .$ (Given C = 150 $μ F$ ) [2024]

[IMAGE 184]

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(400)

$V_{A} + \frac{10}{3} (1) - 6 (1) = V_{B}$

[IMAGE 185]

$V_{A} - V_{B} = 6 - \frac{10}{3} = \frac{8}{3} volt$

$Q = C (V_{A} - V_{B}) = 150 \times \frac{8}{3} = 400 μ C$

Q 3 :
In the given figure, the charge stored in $6 μ F$ capacitor, when points A and B are joined by a connecting wire is ______ $μ C$ [2024]

[IMAGE 186]

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(36)

At steady state, capacitor behaves as an open circuit and current flows in circuit as shown in the diagram.

[IMAGE 187]

$R_{eq} = 9 Ω$

$i = \frac{9 V}{9 Ω} = 1 A$

$Δ V_{6 Ω} = 1 \times 6 = 6 V$

$V_{A} = 3 V$

So, potential difference across $6 μ F$ is 6 V.

Hence $Q = C Δ V = 6 \times 6 \times 10^{- 6} C = 36 μ C$

Q 4 :
In an electrical circuit drawn below the amount of charge stored in the capacitor is ________ $μ C$ . [2024]

[IMAGE 188]

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(60)

[IMAGE 189]

$i_{net} = \frac{Δ V}{R_{eq}}$

$= \frac{Δ V}{R_{eq}} = \frac{V}{R_{1} + R_{3}} = \frac{10}{4 + 6} = 1 A$

$V_{A}' - V_{B}' = i R_{3} = 1 \times 6 = 6 V$

$q = C Δ V = C (V_{A} - V_{B}) = 10 \times 6 = 60 μ C$

Topic Question Set

Q 1 :
The electric field between the two parallel plates of a capacitor of 1.5 $μ F$ capacitance drops to one third of its initial value in 6.6 $μ s$ when the plates are connected by a thin wire.

The resistance of this wire is __________ $Ω .$ (Given, log 3 = 1.1) [2024]

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Q 2 :
The charge accumulated on the capacitor connected in the following circuit is ___________ $μ C .$ (Given C = 150 $μ F$ ) [2024]

[IMAGE 184]

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Q 3 :
In the given figure, the charge stored in $6 μ F$ capacitor, when points A and B are joined by a connecting wire is ______ $μ C$ [2024]

[IMAGE 186]

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Q 4 :
In an electrical circuit drawn below the amount of charge stored in the capacitor is ________ $μ C$ . [2024]

[IMAGE 188]

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Topic Question Set

Q 1 : The electric field between the two parallel plates of a capacitor of 1.5 μF capacitance drops to one third of its initial value in 6.6 μs when the plates are connected by a thin wire. The resistance of this wire is __________ Ω. (Given, log 3 = 1.1) [2024]

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Q 2 : The charge accumulated on the capacitor connected in the following circuit is ___________ μC. (Given C = 150 μF) [2024] [IMAGE 184]

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Q 3 : In the given figure, the charge stored in 6μF capacitor, when points A and B are joined by a connecting wire is ______ μC [2024] [IMAGE 186]

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Q 4 : In an electrical circuit drawn below the amount of charge stored in the capacitor is ________ μC. [2024] [IMAGE 188]

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Q 1 :
The electric field between the two parallel plates of a capacitor of 1.5 $μ F$ capacitance drops to one third of its initial value in 6.6 $μ s$ when the plates are connected by a thin wire.

The resistance of this wire is __________ $Ω .$ (Given, log 3 = 1.1) [2024]

Q 2 :
The charge accumulated on the capacitor connected in the following circuit is ___________ $μ C .$ (Given C = 150 $μ F$ ) [2024]

[IMAGE 184]

Q 3 :
In the given figure, the charge stored in $6 μ F$ capacitor, when points A and B are joined by a connecting wire is ______ $μ C$ [2024]

[IMAGE 186]

Q 4 :
In an electrical circuit drawn below the amount of charge stored in the capacitor is ________ $μ C$ . [2024]

[IMAGE 188]