Question

Input of a transformer is connected to$12V,24W$ a.c. Supply .Transformation ratio of the transformer is $20.$If efficiency of the transformer is $90\%$ calculate (i) Input current, (ii) Output potential and (iii) Output current.

Answer 1

Step 1:- Given data

Input voltage $E_p=12volts$

Input power $P_{input}=24W$

Transformation ratio $r=20$

Efficiency of transformer $\eta =90\%$

Step 2:- Finding input current

Let the input current is $I_{input}$

$$\begin{gathered} P_{input}=E_p\times I_{input} \\ {I}_{input}=\frac{P_{input}}{E_p} \\ {I}_{input}=\frac{24}{12} \\ {I}_{input}=2A \end{gathered}$$

Hence, the input current is $2A.$

Step 3:- Finding output potential

Let the output potential is $E_s$

$$\begin{gathered} Weknownthatthetransformationratiois \\ r=\frac{E_s}{E_p} \\ \frac{E_S}{E_P}=20 \\ \frac{E_S}{12}=20 \\ {E}_S=240volts \end{gathered}$$

Hence, output potential is $240volts.$

Step 4 :- Finding output power

Efficiency of transformer is $\eta =90\%$

$$\begin{gathered} \eta =\frac{Outputpower\left(P_{output}\right)}{Inputpower\left(P_{input}\right)}\times 100 \\ 90=\frac{P_{output}}{24}\times 100 \\ {P}_{output}=\frac{90\times 24}{100} \\ {P}_{output}=21.6W \end{gathered}$$

Step 5:- Finding output current

Let the output current is $I_{output}$

$$\begin{gathered} I_{output}=\frac{P_{output}}{E_s} \\ {I}_{output}=\frac{21.6}{240} \\ {I}_{output}=0.09A \end{gathered}$$

Hence, output current is $0.09A.$