Three resistors having resistances \(r_1, r_2~\text{and}~r_3\) are connected as shown in the given circuit. The ratio \(\frac{i_3}{i_1}\) of currents in terms of resistances used in the circuit is:

  
1. \(\frac{r_1}{r_1+r_2}\)
2. \(\frac{r_2}{r_1+r_3}\)
3. \(\frac{r_1}{r_2+r_3}\)
4. \(\frac{r_2}{r_2+r_3}\)

The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section, and same material is \(0.25~\Omega\). What will be the effective resistance if they are connected in series?
1. \(1~\Omega\) 
2. \(4~\Omega\)
3. \(0.25~\Omega\)
4. \(0.5~\Omega\)

In a potentiometer circuit, a cell of emf \(1.5~\text{V}\) gives a balance point at 36 cm length of wire. If another cell of emf 2.5 V replaces the first cell, then at what length of the wire, the balance point occur? 
1. 64 cm 
2. 62 cm 
3. 60 cm 
4. 21.6 cm

Match Column I and Column II with appropriate relations.

The equivalent resistance between \(A\) and \(B\) for the mesh shown in the figure is:

For the circuit given below, Kirchhoff's loop rule for the loop \(BCDEB\) is given by the equation:

Two solid conductors are made up of the same material and have the same length and the same resistance. One of them has a circular cross-section of area \(  𝐴 _1\) and the other one has a square cross-section of area \(A_2.\) The ratio of \(𝐴 _1 / 𝐴 _2  \) is:

For the circuit shown in the figure, the current \(I\) will be: