Problem 58 - Master Resource Book in JEE Main Physics

Question

The ratio of turns in primary and secondary coils of a transformer is \(1: 20 .\) The ratio of currents in primary and secondary coils will be (a) \(1: 20\) (b) \(20: 1\) (c) \(1: 400\) (d) \(400: 1\) A

Step-by-Step Solution

Answer

(b) 20: 1

Step 1: Understanding Transformer Functionality

A transformer works on the principle of electromagnetic induction and it is used to increase or decrease alternating voltages and currents. The turns ratio plays a crucial role in determining how voltage and current change across the transformer.

Step 2: Given Information

We know that the ratio of the number of turns in the primary (\(n_p\)) and secondary (\(n_s\)) coils is \(1: 20\), which means that if \(n_p = 1\), then \(n_s = 20\).

Step 3: Understanding Turn and Current Relationship

In an ideal transformer, the ratio of the currents in the primary (\(I_p\)) and secondary (\(I_s\)) coils is inversely related to the turns ratio. This can be expressed as:\[\frac{I_p}{I_s} = \frac{n_s}{n_p}\]This formula indicates that when the number of turns increases, the current decreases, and vice versa.

Step 4: Apply the Turns and Current Relationship

Plug in the given values:\[\frac{I_p}{I_s} = \frac{20}{1}\]Thus, the ratio of the currents is \(I_p: I_s = 20: 1\).

Key Concepts

Turns Ratio

In a transformer, the turns ratio is vital in determining how the device adjusts voltage and current levels between its two coils. It represents the ratio of the number of windings, or turns, in the primary coil to the number of windings in the secondary coil.
For example, a turns ratio of 1:20 means there is one turn on the primary coil for every twenty turns on the secondary coil. This ratio directly influences how much the voltage will step up or step down.

• A large turns ratio can significantly increase voltage.
• A small turns ratio leads to a minor voltage change.

This ratio is not only crucial for voltage transformation but also plays a role in determining how currents are distributed across the transformer.

Electromagnetic Induction

Electromagnetic induction is the underlying principle that allows transformers to function. Discovered by Michael Faraday, it describes how an electric current can be generated in a coil by changing the magnetic field around it. When alternating current flows through the primary coil, it creates a changing magnetic field.
This changing magnetic field passes through the secondary coil, inducing a voltage due to Faraday's law of electromagnetic induction.

• The greater the rate of change of the magnetic field, the higher the induced voltage.
• Electromagnetic induction enables energy transfer without a direct electrical connection between the coils.

Without electromagnetic induction, transformers would not be able to efficiently convert voltages from one level to another.

Primary and Secondary Coils

A transformer consists of two main components: the primary coil and the secondary coil. These coils are essential for transferring and transforming electrical energy. The primary coil is connected to the input voltage source, while the secondary coil connects to the output load.

• The primary coil receives electrical energy and creates a magnetic field through which the energy is transferred.
• The secondary coil captures this energy, inducing a voltage according to its number of turns relative to the primary.

This relationship between the coils allows the transformer to either step up or step down voltage levels. The primary and secondary coils work together via electromagnetic induction to achieve efficient energy transfer.

Current Transformation

In a transformer, current transformation is as important as voltage transformation. The turns ratio not only affects the voltage but also determines the relationship between the currents in the primary and secondary coils. According to the formula:\[\frac{I_p}{I_s} = \frac{n_s}{n_p}\]This shows that the current in the primary coil \(I_p\) and the current in the secondary coil \(I_s\) are inversely proportional to their respective turns. If the transformer increases voltage (step-up), the secondary current \(I_s\) decreases, and vice versa.

• A transformer with a turns ratio of 1:20 will have a current ratio of 20:1.
• This means for every unit of current in the secondary coil, the primary coil has 20 units of current.

Understanding this concept is essential for designing circuits that require specific current and voltage levels.