Question

A transformer has $250$ primary turns and $500$ secondary turns. If $200V$ electric potential is applied to the primary resulting in a current of $5mA$, find the secondary voltage and current.

Answer 1

Step 1: Given data

Number of turns in the primary coil $N_p=250$

Number of turns in the secondary coil $N_s=500$

Input voltage in the primary coil is $V_p=200V$

Input current in the primary coil is $i=5mA$

where $N_s$ and $N_p$is the number of turns in the secondary coil and primary coil respectively, $V_s$ and $V_p$ is voltage in the secondary and primary coil of the transformer and, $i_s$ and $i_p$ is current in the secondary and primary coil of the transformer.

Step 2: Finding secondary voltage

We know that,

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

Substituting given values in the above formula

$\frac{500}{250}=\frac{V_s}{200}$

Cross multiply

$$\begin{gathered} V_s=\frac{500}{250}\times 200 \\ {V}_s=400V \end{gathered}$$

Step 3: Finding secondary current

We know that.

Input power = Output power i.e.,

$V_p{i}_p=V_s{i}_s$

Substituting given values in the above formula

$$\begin{gathered} 200\times 5=400\times i_s \\ {i}_s=\frac{200\times 5}{400} \\ {i}_s=2.5mA \end{gathered}$$

Hence, the $2.5mA$secondary voltage is $400V$and the secondary current is $2.5mA$.