Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1mm. Conductor B is a hollow tube of outer diameter 2mm and inner diameter 1mm. Find the ratio of resistance R_A to R_B.

The circuit in Fig 3.6 shows two cells connected in opposition to each other. Cell E₁ is of emf 6V and internal resistance 2 Ω; the cell E₂ is of emf 4V and internal resistance 8Ω. Find the potential difference between the points A and B.

Two cells of same emf E but internal resistance r₁ and r₂ are connected in series to an external resistor R (Fig 3.7). What should be the value of R so that the potential difference across the terminals of the first cell becomes zero.

Suppose there is a circuit consisting of only resistances and batteries and we have to double (or increase it to n-times) all voltages and all resistances. Show that currents are unaltered. Do this for circuit of Example 3.7 in the NCERT Text Book for Class XII.

Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ωrespectively, are connected in parallel with the positive end of 10V battery connected to negative pole of 2V battery (Fig 3.8). Find the effective voltage and effective resistance of the combination.