Question

A transformer of efficiency $90\%$ draws an input power of $4kW$. An electrical appliance connected across the secondary draws a current of $6A$. The impedance of the device is

• A. $60\Omega$
• B. $50\Omega$
• C. $80\Omega$
• D. $100\Omega$
• E. $120\Omega$

Answer 1

The correct option is D

$100\Omega$

Step1: Given data and assumptions.

Input power, $P_{in}=4kW=4000W$

Secondary current, $I_s=6A$

Efficiency, $\eta =90\%$

Step1: Find the output power.

Formula used:

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

Where, $\eta$ is the efficiency, $P_{out}$ is the output power, $P_{in}$ is the input power.

Now,

$\Rightarrow$$90\%=\frac{P_{out}}{4000}$

$\Rightarrow$$\frac{90}{100}=\frac{P_{out}}{4000}$

$\Rightarrow$$P_{out}=3600W$

Step3: Find the impedance of the device.

We know that,

$P_{out}=Z{i}^2$

Where $Z$ is the impedance and $i$ is the current.

Now,

$\Rightarrow$$Z=\frac{P_{out}}{i^2}$

$\Rightarrow$$Z=\frac{3600}{6^2}$

$\Rightarrow$$Z=100\Omega$

Hence, option D is correct.