Question

A step-up transformer has a primary coil with 100 turns and a secondary coil with 25 turns. If the input voltage in the primary coil is 40 volts, what is the output voltage reduced to in the secondary coil?


35 volts

20 volts

10 volts

4 volts

Answer 1

In a transformer, the relationship between the number of turns in the coils and the voltage is given by the formula:

\[
\frac{V_p}{V_s} = \frac{N_p}{N_s}
\]

where:

- \( V_p \) = voltage across the primary coil
- \( V_s \) = voltage across the secondary coil
- \( N_p \) = number of turns in the primary coil
- \( N_s \) = number of turns in the secondary coil

Given:
- \( N_p = 100 \) turns
- \( N_s = 25 \) turns
- \( V_p = 40 \) volts

We want to find \( V_s \):

\[
\frac{40}{V_s} = \frac{100}{25}
\]

Calculating the right side:

\[
\frac{100}{25} = 4
\]

Now we can write the equation:

\[
\frac{40}{V_s} = 4
\]

Now, cross-multiply to solve for \( V_s \):

\[
40 = 4 \times V_s
\]

Now, divide both sides by 4:

\[
V_s = \frac{40}{4} = 10 \text{ volts}
\]

Thus, the output voltage in the secondary coil is **10 volts**.