Previous Year NEET Question- Transformers

Question 1#

In an ideal transformer, the ratio of the number of turns in the primary coil to the secondary coil is $n_1:n_2$. If $V_1$ and $I_1$ are the voltage and current in the primary coil, and $V_2$ and $I_2$ are the voltage and current in the secondary coil respectively, which of the following relations is incorrect?

• (1) $V_2/V_1 = n_2/n_1$
• (2) $I_2/I_1 = n_1/n_2$
• (3) $V_1 I_1 = V_2 I_2$
• (4) $V_1/V_2 = I_2/I_1$

Solution:

For an ideal transformer, the power in the primary coil is equal to the power in the secondary coil. This gives us the relation:

$V_1 I_1 = V_2 I_2$

From this, we can derive:

$V_1/V_2 = I_2/I_1$

Also, the voltage and current ratios are related to the turns ratio as follows:

$V_2/V_1 = n_2/n_1$ (Voltage is directly proportional to the number of turns) $I_2/I_1 = n_1/n_2$ (Current is inversely proportional to the number of turns)

All the given relations (1), (2), and (3) are correct for an ideal transformer. Therefore, the incorrect relation is (4).

Answer: (4)

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Question 2#

A step-down transformer reduces the voltage from 2200 V to 220 V. If the power output of the transformer is 4.4 kW and its efficiency is 90%, what is the power input to the primary coil?

• (1) 4.88 kW
• (2) 4.44 kW
• (3) 4.00 kW
• (4) 3.96 kW

Solution:

The efficiency ($\eta$) of a transformer is given by the ratio of the output power ($P_{out}$) to the input power ($P_{in}$):

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

We are given: $P_{out} = 4.4 , \text{kW} = 4400 , \text{W}$ $\eta = 90% = 0.90$

We need to find the power input $P_{in}$. Rearranging the efficiency formula, we get:

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

Substituting the given values:

$P_{in} = \frac{4400 , \text{W}}{0.90} = \frac{44000}{9} , \text{W} \approx 4888.89 , \text{W}$

Converting this to kilowatts:

$P_{in} \approx 4.889 , \text{kW}$

Rounding to two decimal places, the power input is approximately 4.89 kW. The closest option is 4.88 kW.

Answer: (1)