Sure! To calculate the voltage output by the secondary winding of a transformer, you can use the transformer voltage equation. Here are the detailed steps:
1. Understanding the relationship:
The transformer voltage equation relates the primary and secondary voltages to the number of turns in the primary and secondary windings. The equation is:
[tex]\[
\frac{V_p}{V_s} = \frac{N_p}{N_s}
\][/tex]
Where:
- [tex]\(V_p\)[/tex] is the primary voltage
- [tex]\(V_s\)[/tex] is the secondary voltage
- [tex]\(N_p\)[/tex] is the number of turns in the primary winding
- [tex]\(N_s\)[/tex] is the number of turns in the secondary winding
2. Given values:
- Primary voltage ([tex]\(V_p\)[/tex]) = 50 V
- Number of turns in primary winding ([tex]\(N_p\)[/tex]) = 400 turns
- Number of turns in secondary winding ([tex]\(N_s\)[/tex]) = 1500 turns
3. Rearranging the formula to solve for [tex]\(V_s\)[/tex]:
[tex]\[
V_s = V_p \times \frac{N_s}{N_p}
\][/tex]
4. Substituting the given values into the equation:
[tex]\[
V_s = 50 \, \text{V} \times \frac{1500 \, \text{turns}}{400 \, \text{turns}}
\][/tex]
5. Performing the division:
[tex]\[
\frac{1500}{400} = 3.75
\][/tex]
6. Multiplying by the primary voltage:
[tex]\[
V_s = 50 \, \text{V} \times 3.75
\][/tex]
7. Calculating the final value:
[tex]\[
V_s = 187.5 \, \text{V}
\][/tex]
So, the voltage output by the secondary winding of the transformer is 187.5 V.
