Question

A transformer has an efficiency of $80\%$. It is connected to a power input of $5kW$ at $200V$. If the secondary voltage is $250V$, the primary and secondary currents are respectively

• A. $25A$, $20A$
• B. $20A$,$16A$
• C. $25A$, $16A$
• D. $40A$, $25A$
• E. $40A$, $16A$

Answer 1

The correct option is C

$25A$, $16A$

Step1: Given data and assumptions.

Efficiency, $\eta =80\%$

Input power, $P_{in}=5kW=5000W$

Input voltage, $V_{in}=200V$

Output voltage, $V_{out}=250V$

Step2: Find the primary current.

Formula used:

Current, $I=\frac{P}{V}$

Where $P$ is the power and $V$ is the voltage.

And

Efficiency, $\eta =\frac{P_{out}}{P_{in}}$

Since,

$I_p=\frac{P_{in}}{V_{in}}$

Where $I_p$ is the primary current

$\Rightarrow$$I_p=\frac{5000}{200}$

$\Rightarrow$$I_p=25A$

Step3: Find the Secondary current.

We have.

$\eta =\frac{P_{out}}{P_{in}}$

$\Rightarrow$$80\%=\frac{P_{out}}{5000}$

$\Rightarrow$$80\%=\frac{V_{out}{I}_s}{5000}$

Where $I_s$ is the secondary current

$\Rightarrow$$\frac{80}{100}=\frac{250I_s}{5000}$

$\Rightarrow$ $I_s=16A$

Hence, option C is correct.