A power transmission line feeds input power at 2300 V to a step-down transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V.

Question

Accepted Answer

The correct option is (2):

To determine the number of turns in the secondary coil of a transformer, we use the transformer equation, which relates the voltages and the number of turns in the primary and secondary coils. The relationship is given by:
$\frac{V\_P}{V\_S} = \frac{N\_P}{N\_S}$
Where:
$V\_P$ = primary voltage
$V\_S$ = secondary voltage
$N\_P$ = number of turns in the primary coil
$N\_S$ = number of turns in the secondary coil

From the question, we are given:
Input power (primary voltage), $V\_P = 2300 \mathrm{\~V}$
Number of turns in the primary windings, $N\_P = 4000$ turns
Output power (secondary voltage), $V\_S = 230 \mathrm{\~V}$

We need to find $N\_S$. Rearranging the formula to solve for $N\_S$:
$N\_S = N\_P 	imes \frac{V\_S}{V\_P}$

Now, substitute the given values into the equation:
$N\_S = 4000 	imes \frac{230 \mathrm{\~V}}{2300 \mathrm{\~V}}$
$N\_S = 4000 	imes \frac{1}{10}$
$N\_S = 400$ turns

Therefore, the number of turns in the secondary coil should be 400 to get an output power at 230 V. This is a step-down transformer, meaning the secondary voltage is lower than the primary voltage, and consequently, the number of turns in the secondary coil should be less than in the primary coil, which our calculation confirms.

The incorrect option is (1): 40
This option would result in an even lower secondary voltage, as the ratio of secondary to primary turns would be significantly smaller ($40/4000 = 1/100$), leading to $23 \mathrm{\~V}$ output.

The incorrect option is (3): 4
This option represents a severe step-down, yielding an output voltage of only $2.3 \mathrm{\~V}$ ($4/4000 = 1/1000$). This is not the desired $230 \mathrm{\~V}$.

The incorrect option is (4): 4000
This option implies no voltage change ($V\_S = V\_P$) if the number of turns were equal, or it would mean that the transformer is not stepping down the voltage as required. A step-down transformer must have fewer turns in the secondary coil than in the primary coil.