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.

Consider a circuit with effective emf E_eff, effective internal resistance R_eff and total resistance R as shown in the figure.

The current in this circuit =

If we increase all the values in the circuit by n, effective emf is nE_eff, effective internal resistance is nR_eff and total resistance is nR.

The current in the final circuit = =