Kirchhoff’s Laws

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.

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?

Twelve wires, each of equal resistance r, are joined to form a cube, as shown in the figure. Find the equivalent resistance between the diagonally-opposite points a and f.

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:

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:

Determine the equivalent resistance of networks shown in Fig.

Kirchhoff's voltage law and current law are respectively in accordance with the conservation of .................................. .

1. charge and momentum
2. charge and energy
3. energy and charge
4. energy and momentum

Two unequal resistances, R₁ and R_2, 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?