Advertisements
Advertisements
प्रश्न
A capacitor of capacitance 8.0 μF is connected to a battery of emf 6.0 V through a resistance of 24 Ω. Find the current in the circuit (a) just after the connections are made and (b) one time constant after the connections are made.
Advertisements
उत्तर
Given:-
Capacitance, C = 8 μF
Emf of the battery, V= 6 V
Resistance, R = 24
(a) Just after the connections are made, there will be no charge on the capacitor and, hence, it will act as a short circuit. Current through the circuit,
\[i = \frac{V}{R} = \frac{6}{24} = 0 . 25 A\]
(b) The charge growth on the capacitor,
\[q = Q \left( 1 - e^{- \frac{t}{RC}} \right)\]
One time constant = RC = 8 × 24 = 192 × 10-6 s
For t = RC, we have:-
\[q = Q . \left( 1 - e^\frac{- RC}{RC} \right)\]
\[ \Rightarrow q = CV\left( 1 - e^{- 1} \right)\]
\[ \Rightarrow q = 8 \times {10}^{- 6} \times 6 \times 0 . 632\]
\[ = 3 . 036 \times {10}^{- 5} C\]
\[V = \frac{Q}{C} = \frac{3 . 036 \times {10}^{- 5}}{8 \times {10}^{- 6}} = 3 . 792 V\]
Applying KVL in the circuit, we get:-
E = V + iR
⇒ 6 = 3.792 + 24i
⇒ i = 0.09 A
APPEARS IN
संबंधित प्रश्न
Kirchhoff's voltage law and current law are respectively in accordance with the conservation of .................................. .
- charge and momentum
- charge and energy
- energy and charge
- energy and momentum
State the two Kirchhoff’s rules used in electric networks. How are there rules justified?
State Kirchhoff's rules and explain on what basis they are justified.
Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of (11/3) Ω?
Consider the potentiometer circuit as arranged in the figure. The potentiometer wire is 600 cm long. (a) At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer? (b) If the jockey touches the wire at a distance of 560 cm from A, what will be the current in the galvanometer?
Twelve wires each having a resistance of 3 Ω are connected to form a cubical network. A battery of 10 V and negligible internal resistance is connected across the diagonally opposite corners of this network. Determine its equivalent resistance and the current along each edge of the cube.
State and explain Kirchhoff’s rules.
Obtain the condition for bridge balance in Wheatstone’s bridge.
Explain the determination of unknown resistance using meter bridge.
How the emf of two cells are compared using potentiometer?
In a potentiometer arrangement, a cell of emf 1.25 V gives a balance point at 35 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 63 cm, what is the emf of the second cell?
Figure shows current in a part of an electrical circuit. Then current I is ______.
Assertion: Kirchhoff’s junction rule follows from conservation of charge.
Reason: Kirchhoff’s loop rule follows from conservation of momentum.
The Kirchhoff's second law (ΣiR = ΣE), where the symbols have their usual meanings, is based on ______.
Kirchhoff s second law is based on the law of conservation of ______
The circuit in figure shows two cells connected in opposition to each other. Cell E1 is of emf 6V and internal resistance 2Ω; the cell E2 is of emf 4V and internal resistance 8Ω. Find the potential difference between the points A and B.
Derive the equation of the balanced state in a Wheatstone bridge using Kirchhoff’s laws.
The value of current in the 6Ω resistance is ______.
In the circuit shown in Figure below, E1 and E2 are batteries having emfs of 25V and 26V. They have an internal resistance of 1 Ω and 5 Ω respectively. Applying Kirchhoff’s laws of electrical networks, calculate the currents I1 and I2.
