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 junction law is equivalent to .............................
(a) conservation of energy.
(b) conservation of charge
(c) conservation of electric potential
(d) conservation of electric flux
Use Kirchhoff's rules to obtain conditions for the balance condition in a Wheatstone bridge.
The current is drawn from a cell of emf E and internal resistance r connected to the network of resistors each of resistance r as shown in the figure. Obtain the expression for
- the current draw from the cell and
- the power consumed in the network.
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?
Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of (6/11) Ω?
Determine the equivalent resistance of networks shown in Fig.
Determine the equivalent resistance of networks shown in Fig.
Calculate the value of the resistance R in the circuit shown in the figure so that the current in the circuit is 0.2 A. What would b the potential difference between points A and B?
Consider the following two statements:-
(A) Kirchhoff's junction law follows from conservation of charge.
(B) Kirchhoff's loop law follows from conservative nature of electric field.
On which conservation principle is Kirchoff's Second Law of electrical networks based?
In the circuit shown in the figure below, E1 and E2 are two cells having emfs 2 V and 3 V respectively, and negligible internal resistance. Applying Kirchhoff’s laws of electrical networks, find the values of currents l1 and I2.
State Kirchhoff’s current rule.
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?
A copper wire of 10-6 m2 area of cross-section, carries a current of 2 A. If the number of electrons per cubic meter is 8 × 1028, calculate the current density and average drift velocity.
The Kirchhoff's second law (ΣiR = ΣE), where the symbols have their usual meanings, is based on ______.
The e.m.f of The battery in a thermocouple is doubled. The rate of heat generated at one of the junction will.
The figure below shows current in a part of electric circuit. The current I is ______.
Kirchhoff s second law is based on the law of conservation of ______
Three resistors having resistances r1, r2 and r3 are connected as shown in the given circuit. The ratio `i_3/i_1` of currents in terms of resistances used in the circuit is:
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.
Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ω respectively, are connected in parallel with the positive end of 10V battery connected to negative pole of 2V battery (Figure). Find the effective voltage and effective resistance of the combination.
State the two Kirchhoff’s rules used in the analysis of electric circuits and explain them.
The value of current in the 6Ω resistance is ______.
A 6-volt battery is connected to the terminals of a three-metre-long wire of uniform thickness and resistance of 100 ohms. The difference of potential between two points on the wire separated by a distance of 50 cm will be ______.
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.
The figure below shows two batteries, E1 and E2, having emfs of 18V and 10V and internal resistances of 1 Ω and 2 Ω, respectively. W1, W2 and W3 are uniform metallic wires AC, FD and BE having resistances of 8 Ω, 6 Ω and 10 Ω respectively. B and E are midpoints of the wires W1 and W2. Using Kirchhoff's laws of electrical circuits, calculate the current flowing in the wire W3:
A constant voltage of 50 V is maintained between the points A and B of the circuit shown in the figure. The current through the branch CD of the circuit is:
