Question

A generator supplies 100 V to a transformer’s primary coil, which has50turns. If the secondary coil has 500 turns, what is the secondary voltage?

Short answer

The secondary voltage is $1.00\times {10}^{3}V$.

Step-by-step solution

Listing the given quantities:

Primary voltage is $V_p=100V$.

Number of turns in primary coil is $N_p=50$.

Number of turns in secondary coil is role="math" localid="1663223267436" ${\mathrm{N}}_s=500$.

Understanding the relationship between the voltage and the number of turns:

The number of turns on the primary winding divided by the number of turns on the secondary coil is the turns ratio of the transformer. The turns ratio of the transformer affects the expected function of the transformer as well as the required voltage on the secondary winding.

Explanation:

Write the equation that shows the relation between the voltages, and the number of turns as below.

$\frac{V_s}{V_p}=\frac{N_s}{N_p}$

Rearranging it for $V_s$, and you have

$$\begin{gathered} V_s=V_p\frac{N_s}{N_p} \\ =\left(100\right)\frac{500}{50} \\ =1.00\times {10}^{3}V \end{gathered}$$

Hence, the secondary voltage is $1.00\times {10}^{3}V$.