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Find the equivalent resistances of the networks shown in the figure between the points a and b.





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An infinite ladder is constructed with 1 Ω and 2 Ω resistors, as shown in the figure. (a) Find the effective resistance between the points A and B. (b) Find the current that passes through the 2 Ω resistor nearest to the battery.

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An infinite ladder is constructed with 1 Ω and 2 Ω resistors, as shown in the figure. (a) Find the effective resistance between the points A and B. (b) Find the current that passes through the 2 Ω resistor nearest to the battery.

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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?

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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?

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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.
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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.
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Two unequal resistances, R1 and R2, are connected across two identical batteries of emf ε and internal resistance r (see the figure). Can the thermal energies developed in R1 and R2 be equal in a given time? If yes, what will be the condition?

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Two unequal resistances, R1 and R2, are connected across two identical batteries of emf ε and internal resistance r (see the figure). Can the thermal energies developed in R1 and R2 be equal in a given time? If yes, what will be the condition?

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A long bar magnet has a pole strength of 10 Am. Find the magnetic field at a point on the axis of the magnet at a distance of 5 cm from the north pole of the magnet.
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An electric dipole of dipole moment `vecP` is placed in a uniform electric field `vecE` with its axis inclined to the field. Write an expression for the torque `vecT` experienced by the dipole in vector form. Show diagrammatically how the dipole should be kept in the electric field so that the torque acting on it is:
- maximum
- Zero
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Solve the following question.
Using Kirchhoff’s rules, calculate the current through the 40 Ω and 20 Ω resistors in the following circuit.

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Solve the following question.
Using Kirchhoff’s rules, calculate the current through the 40 Ω and 20 Ω resistors in the following circuit.

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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.
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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.
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Deduce the expression for the torque `vec"τ"` acting on a planar loop of area `vec"A"` acting on a planar loop of area `vec"B"`. If the loop is free to rotate, what would be its orientation in stable equilibrium?
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Define electrostatic potential at a point. Write its S.I. unit. Three-point charges q1, q2 and q3 are kept respectively at points A, B, and C as shown in the figure, Derive the expression for the electrostatic potential energy of the system.

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A point charge is placed at the centre of a hollow conducting sphere of internal radius ‘r’ and outer radius ‘2r’. The ratio of the surface charge density of the inner surface to that of the outer surface will be ______.
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Derive the expression for the torque acting on an electric dipole, when it is held in a uniform electric field. identify the orientation of the dipole in the electric field, in which it attains a stable equilibrium.
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A short bar magnet of magnetic moment m = 0.32 J T–1 is placed in a uniform magnetic field of 0.15 T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its
- stable, and
- unstable equilibrium?
What is the potential energy of the magnet in each case?
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