A step-up transformer has 26 turns on the primary coil and 720 turns on the secondary coil. If this transformer is to produce an output of 4100 V with a 16-mA current, what input current and voltage are needed?
The input current and voltage needed are 443 mA and 148 V respectively.
In a step-up transformer, the relationship between the number of turns in its primary coil ([tex]N_{p}[/tex]), the number of turns in its secondary coil ([tex]N_{s}[/tex]), the input voltage ([tex]V_{p}[/tex]), the output voltage ([tex]V_{s}[/tex]), the input current ([tex]I_{p}[/tex]), and the output current ([tex]I_{s}[/tex]) is given by;
[tex]\frac{N_{s} }{N_{p} }[/tex] = [tex]\frac{V_{s} }{V_{p} }[/tex] = [tex]\frac{I_{p} }{I_{s} }[/tex]
This implies that;
[tex]\frac{N_{s} }{N_{p} }[/tex] = [tex]\frac{V_{s} }{V_{p} }[/tex] ---------------------(i)
[tex]\frac{N_{s} }{N_{p} }[/tex] = [tex]\frac{I_{p} }{I_{s} }[/tex] ---------------------(ii)
From the question;
[tex]N_{p}[/tex] = 26 turns
[tex]N_{s}[/tex] = 720 turns
[tex]V_{s}[/tex] = 4100V
[tex]I_{s}[/tex] = 16mA = 16 x 10⁻³A
(a) Substitute these values into equation (ii) as follows;
[tex]\frac{720}{26}[/tex] = [tex]\frac{I_{p} }{16*10^{-3}}[/tex]
Solve for [tex]I_{p}[/tex];
[tex]I_{p}[/tex] = 720 x 16 x 10⁻³ / 26
[tex]I_{p}[/tex] = 443 x 10⁻³
[tex]I_{p}[/tex] = 443 mA
Therefore the input current needed is 443mA
(b) Also, substitute those values into equation (i) as follows;
[tex]\frac{720}{26}[/tex] = [tex]\frac{4100 }{V_{p} }[/tex]
Solve for [tex]V_{p}[/tex];
[tex]V_{p}[/tex] = 4100 x 26 / 720
[tex]V_{p}[/tex] = 148 V
Therefore, the input current needed is 148 V
