Suppose that you want to build a transformer that will convert 70 V power coming in the primary coil to 245 V power going out of the secondary coil. What is the smallest total number of turns (primary turns plus secondary turns) you need to create the transformer?
A) 63
B) 9
C) 7
D) 315
The ratio of voltage in a transformer is equal to the ratio of the number of turns in the coils. In this case, the primary voltage is 70 V and the secondary voltage is 245 V.
So, the ratio of turns = ratio of voltage = 245/70 = 3.5
Since the total number of turns is equal to the sum of the primary turns and secondary turns, we can say:
Let the primary turns be x and secondary turns be 3.5x (from the ratio calculated above).
So, x + 3.5x = total number of turns
4.5x = total number of turns
To find the smallest total number of turns, we need to find the smallest integer solution for x.
Since x must be a whole number, x = 7 and the total number of turns = 4.5 * 7 = 31.5.
Since the number of turns must be a whole number, we need to round up to the nearest whole number. So, the smallest total number of turns required to build the transformer is 32.
Therefore, the answer is not included in the given options A) 63, B) 9, C) 7, D) 315.