Question

The transformation ratio in the step-up transformer is

• A. one
• B. greater than one
• C. less than one
• D. the ratio greater or less than one depends on the other factors

Answer 1

The correct option is B

greater than one

Explanation for the correct answer:-

Option (B)

Step 1: Formula Used,
Transformation Ratio = $\frac{V_s}{V_p}=\frac{N_2}{N_1}$

$V_s=-N_2\frac{d\varphi }{dt}$, $V_p=-N_1\frac{d\varphi }{dt}$

${\displaystyle \frac{d\varphi }{dt}}$ is the rate of change of magnetic flux.

The number of turns in the primary coil is $N_1$and the number of turns in the secondary coil is $N_2$.

$$V_p$$= Primary voltage

$$V_s$$= Secondary voltage

Step 2: Calculating the transformation ratio in the step-up transformer,

The transformer consists of two coils wound on a soft-core. They are completely insulated from each other.

The number of turns on these coils are not the same. The number of turns in the primary coil is $N_1$and the number of turns in the secondary coil is $N_2$.
When the input voltage $$V_p$$is applied on the input coil, emf is generated on the second coil due to mutual inductance.
$V_s=-N_2\frac{d\varphi }{dt}$
where ${\displaystyle \frac{d\varphi }{dt}}$ is the rate of change of magnetic flux.
Due to change in the magnetic flux linked to the same coil an emf is induced in the primary coil. This is called a back emf.
$V_p=-N_1\frac{d\varphi }{dt}$
Thus,
$\frac{V_s}{V_p}=\frac{N_2}{N_1}$
This implies that the induced voltage in the secondary coil depends on the ratio of turns in the 2 coils. This ratio is called the transformation ratio.
In a step-up transformer, the output voltage is greater than the input voltage.

In such cases, the transformation ratio,
$\frac{V_s}{V_p}=\frac{N_2}{N_1}>1$
Hence, the correct option is Option B.