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]

0%

(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]

0%

(400)

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

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

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

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]

0%

(36)

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

$R_{eq} = 9 Ω$

$i = \frac{9 V}{9 Ω} = 1 A$

$Δ V_{6 Ω} = 1 \times 6 = 6 V$

$V_{A} = 3 V$

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]

0%

(60)

$i_{net} = \frac{Δ V}{R_{eq}}$

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

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

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

Q 5 :
Identify the valid statements relevant to the given circuit at the instant when the key is closed.

A. There will be no current through resistor R.

B. There will be maximum current in the connecting wires.

C. Potential difference between the capacitor plates A and B is minimum.

D. Charge on the capacitor plates is minimum.

Choose the correct answer from the options given below.: [2025]

C, D only
B, C, D only
A, C only
A, B, D only

1

2

3

4

(2)

Capacitor behaves as a short circuit at t = 0

So current will be maximum.

Charge on capacitor will be zero.

Potential difference across capacitor will be zero.

Q 6 :
At steady state the charge on the capacitor, as shown in the circuit below, is ______ $μ$ C. [2025]

0%

(16)

$i = (\frac{5}{25}) A$

$V_{10 Ω} = V_{c} = \frac{5}{25} \times 10 = 2 V$

$Q = 8 \times 2 = 16 μ C$

Q 7 :
The net current flowing in the given circuit is ______ A. [2025]

0%

(1)

The capacitor behaves as open circuit, $I = \frac{V}{R_{eq}}$

$R_{eq} = 2 Ω$

$\Rightarrow I = \frac{2}{2} = 1 A$

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]

0%

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

0%

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]

0%

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

0%

Q 6 :
At steady state the charge on the capacitor, as shown in the circuit below, is ______ $μ$ C. [2025]

0%

Q 7 :
The net current flowing in the given circuit is ______ A. [2025]

0%

Want Us to Email you About Special Offers & Updates?

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]

0%

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

0%

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]

0%

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

0%

Q 6 : At steady state the charge on the capacitor, as shown in the circuit below, is ______ μC. [2025]

0%

Q 7 : The net current flowing in the given circuit is ______ A. [2025]

0%

Want Us to Email you About Special Offers & Updates?

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]

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]

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

Q 6 :
At steady state the charge on the capacitor, as shown in the circuit below, is ______ $μ$ C. [2025]

Q 7 :
The net current flowing in the given circuit is ______ A. [2025]