Rankers Physics

Transformers: Practice Problem & Solution

Turn ratio of a step-up transformer is 1 : 25. If current in load coil is 2 A, then the current in primary coil will be: (1998)
25 A
50 A
0.25 A
0.5 A

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Transformers. Understanding the underlying formula is key to arriving at the correct answer below:

For an ideal transformer, the current ratio is inversely proportional to the turns ratio: $\frac{I_p}{I_s} = \frac{N_s}{N_p}$.
The step-up turns ratio is $N_p : N_s = 1 : 25$, so $\frac{N_s}{N_p} = 25$.
Primary current $I_p = I_s \times 25 = 2 \times 25 = 50 A$.

Detailed Solution (Best of Understanding Complex Concepts)

Concepts Involved
  • Transformer Principle: A transformer operates on the principle of mutual induction to step up or step down an alternating voltage.
  • Turns Ratio: In a step-up transformer, the voltage is increased, which means the secondary coil has more turns than the primary coil ($N_s > N_p$). The given turn ratio of 1 : 25 represents the ratio of primary turns to secondary turns ($N_p : N_s$).
  • Ideal Transformer Equation: Assuming an ideal transformer with 100% efficiency (no power loss), the input power must equal the output power:
    $$V_p \cdot I_p = V_s \cdot I_s$$
    Because the voltage ratio is directly proportional to the turns ratio ($\frac{V_s}{V_p} = \frac{N_s}{N_p}$), it follows that the current ratio is inversely proportional to the turns ratio:
    $$\frac{I_p}{I_s} = \frac{N_s}{N_p}$$
Step-by-Step Solution
  1. Identify the given variables:
    • Ratio of primary turns to secondary turns ($\frac{N_p}{N_s}$) = $\frac{1}{25}$
    • Current in the load/secondary coil ($I_s$) = 2 A
  2. Apply the inverse relationship formula for current and turns ratio:
    $$\frac{I_p}{I_s} = \frac{N_s}{N_p}$$
  3. Substitute the known values into the equation:
    $$\frac{I_p}{2} = \frac{25}{1}$$
  4. Calculate the primary current ($I_p$):
    $$I_p = 2 \cdot 25$$
    $$I_p = 50 \text{ A}$$

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Assertion (A): If a cylindrical bar magnet is dropped through a metallic pipe, it takes more time to come down a similar unmagnetised cylindrical iron bar dropped through the same metallic pipe. Reason (R): For the magnet, eddy currents are produced in the metallic pipe.  
2. 24. A metallic rod of mass per unit length $0.5 kg m^{-1}$ is lying horizontally on a smooth inclined plane which makes an angle of $30^\circ$ with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction $0.25 T$ is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is (2018)
3. 45. Two coil have a mutual inductance $0.005 H$. The current changes in first coil according to equation $I = I_0 \sin \omega t$ where $I_0 = 2 A$ and $\omega = 100pi rad/sec$. The maximum value of emf in second coil is: (1998)
4. An aeroplane in which the distance between the tips of the wings is \(50\text{ m}\) is flying horizontally with a speed of \(360\text{ km/hr}\) over a place where the vertical component of earth's magnetic field is \(2 \times 10^{-4}\text{ Wbm}^{-2}\). The potential difference between the tips of the wings would be:
5. 3. A 800 turn coil of effective area $0.05 m^2$ is kept perpendicular to a magnetic field of $5 \times 10^{-5} T$. When the plane of the coil is rotated by $90^\circ$ around any of its coplanar axis in $0.1 s$, the emf induced in the coil will be: (2019)