Transformer Efficiency and Secondary Turns Calculation
What are the number of secondary turns and the efficiency of the transformer?
Given data: A transformer with 600 turns in the primary coil is used to change an alternating root mean square (rms) potential difference of 240 V to 12 V. When connected to the secondary coil, a lamp labelled "120 W, 12 V" lights normally. The current in the primary coil is 0.60 A when the lamp is lit. The options for the number of secondary turns and efficiency are:
A. 12000, 99%
B. 30, 99%
C. 12000, 83%
D. 30, 83%
Answer:
The number of secondary turns is 30, and the efficiency of the transformer is 99%. The correct option is B.
To find the number of secondary turns, we can use the transformer turns ratio formula:
Np/Ns = Vp/Vs
where Np is the number of primary turns (600), Ns is the number of secondary turns, Vp is the primary voltage (240 V), and Vs is the secondary voltage (12 V).
600/Ns = 240/12
Ns = 600 * (12/240) = 30 turns
To find the efficiency of the transformer, we first calculate the power in the primary and secondary coils.
Power in primary coil (Pp) = Voltage in primary coil (Vp) × Current in primary coil (Ip)
Pp = 240 V × 0.60 A = 144 W
Power in secondary coil (Ps) = Power rating of the lamp = 120 W
Efficiency = (Power in secondary coil / Power in the primary coil) × 100
Efficiency = (120 W / 144 W) × 100 ≈ 99%