• 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

    Correct Answer: B

    Solution :

                    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.

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