A transfer has 500 turns in its primary coil and 20,000 turns in its secondary coil. An AC voltage with maximum voltage of 100 V is applied to the primary coil. What is the maximum voltage across the secondary coil?

A transformer is a device that either raises (steps up) or lowers (steps down) the voltage to move electrical energy from one alternating current circuit to one or more other circuits.

Number of turns in the primary coil of the transformer, $N_1=500$

Number of turns in the secondary coil of the transfer, $N_2=20,000$

The voltage across the primary coil,$V_1=100\text{V}$

A transformer, which consists of the main coil and a secondary coil, is a device for altering the magnitude of an alternating voltage.

The changing flux due to AC voltage in the primary coil induces an AC voltage in the secondary coil. So the ratio of output to input voltages equals the ratio of the number of turns in the secondary to the number in the primary.

$\begin{array}{l}\frac{V_2}{V_1}=\frac{N_2}{N_1}\\ V_2=\left(\frac{N_2}{N_1}\right)V_1\end{array}$

Substitute known values in the above equation.

$\begin{array}{c}{V}_2=\left(\frac{20,000}{500}\right)100\text{V}\\ =\left(40\right)100\text{V}\\ =\text{4000V}\end{array}$

Hence, the maximum voltage across the secondary coil is $4000V$.