• # question_answer                 A step-up transformer operates on a 230 V line and supplies current of 2A to a load. The ratio of the primary and secondary windings is 1 : 25. The current in the primary coil is:                            A)                 15 A       B)                 50 A       C)                            25 A    D)                            12.5 A

Key Idea: The flux per turn of primary coil must be equal to flux per turn of the secondary coil.                 As per key idea, $\frac{{{\phi }_{p}}}{{{n}_{p}}}=\frac{{{\phi }_{s}}}{{{n}_{s}}}$ or            $\frac{1}{{{n}_{p}}}.\frac{d{{\phi }_{p}}}{dt}=\frac{1}{{{n}_{s}}}\frac{d{{\phi }_{s}}}{dt}$ $\therefore \frac{{{e}_{s}}}{{{e}_{p}}}=\frac{{{n}_{s}}}{{{n}_{p}}}\left( as\,\,\,e\propto \,\frac{d\phi }{dt} \right)$                 For no loss of power,                 ei = constant $\therefore i=\frac{1}{e}\times \text{constant}$ or            $\frac{{{i}_{p}}}{{{i}_{s}}}=\frac{{{e}_{s}}}{{{e}_{p}}}$ or            $\frac{{{i}_{p}}}{{{i}_{s}}}=\frac{{{n}_{s}}}{{{n}_{p}}}$ Here,     $\frac{{{n}_{p}}}{{{n}_{s}}}=\frac{1}{25},\,{{i}_{s}}=2A$ $\therefore \frac{{{i}_{p}}}{2}=\frac{25}{1}$ or            ${{i}_{p}}=25\times 2=50\,A$                 Note:    In step-up transformer ${{n}_{s}}>{{n}_{p}}$. It increases voltage and reduces current.                 In step-down transformer, ${{n}_{p}}>{{n}_{s}}$. It increases current and reduces voltage.