Transformer — Revision Notes

⚡ 30-Second Revision

Principle — Mutual Induction.
Works with — AC only, NOT DC.
Ideal Transformer Equations

- $\frac{V_s}{V_p} = \frac{N_s}{N_p} = k$ (Transformation Ratio) - $\frac{I_s}{I_p} = \frac{N_p}{N_s} = \frac{1}{k}$ - $V_p I_p = V_s I_s$ (Power Conservation)

Types

- Step-up: $N_s > N_p \implies V_s > V_p, I_s < I_p$ - Step-down: $N_s < N_p \implies V_s < V_p, I_s > I_p$

Losses (Real Transformer)

1. Copper Loss: $I^2R$ in windings (minimize with thick copper). 2. Eddy Current Loss: In core (minimize with laminated core). 3. Hysteresis Loss: In core (minimize with soft iron core). 4. Flux Leakage: Magnetic flux not linking (minimize with proper winding).

Efficiency — $\eta = \frac{P_{out}}{P_{in}} \times 100\% = \frac{P_{in} - P_{losses}}{P_{in}} \times 100\%$

2-Minute Revision

Transformers are static devices that change AC voltage levels using mutual induction. They consist of primary and secondary coils wound around a laminated soft iron core. The key relationship is the turns ratio, $k = N_s/N_p$, which dictates voltage transformation: $V_s/V_p = k$.

For an ideal transformer, power is conserved, so $V_p I_p = V_s I_s$, meaning current transforms inversely to voltage ($I_s/I_p = 1/k$). Step-up transformers increase voltage ($k>1$), while step-down transformers decrease it ($k<1$).

Crucially, transformers only work with AC because a changing magnetic flux is required for induction; DC produces a constant flux. Real transformers are not 100% efficient due to energy losses: copper loss ($I^2R$ in windings), eddy current loss (induced currents in the core, minimized by lamination), hysteresis loss (energy to magnetize/demagnetize core, minimized by soft iron), and flux leakage.

Efficiency is calculated as output power divided by input power. Understanding these losses and their minimization techniques is vital for NEET.

5-Minute Revision

A transformer is an indispensable device for AC power systems, operating on the principle of mutual induction to alter voltage and current levels without changing frequency. Its core components are a primary coil, a secondary coil, and a laminated soft iron core. When an alternating voltage is applied to the primary, it generates a changing magnetic flux within the core. This flux links with the secondary coil, inducing an EMF (voltage) in it, as per Faraday's law.

The fundamental relationships for an ideal transformer are: $\frac{V_s}{V_p} = \frac{N_s}{N_p} = k$, where $k$ is the transformation ratio. If $k > 1$, it's a step-up transformer (voltage increases, current decreases); if $k < 1$, it's a step-down transformer (voltage decreases, current increases). Power is conserved in an ideal transformer: $P_{in} = P_{out}$, or $V_p I_p = V_s I_s$. This implies $I_s/I_p = N_p/N_s = 1/k$.

It's critical to remember that transformers *only* work with AC. DC creates a constant magnetic field, leading to no change in flux and thus no induced EMF. Connecting a transformer to DC can damage the primary coil due to its low resistance.

Real transformers are never 100% efficient due to various energy losses:

1
Copper Loss — Heat generated ($I^2R$) in the resistive windings. Minimized by using thick copper wires.
2
Eddy Current Loss — Circulating currents induced in the core, causing heating. Minimized by using a laminated (thin, insulated sheets) soft iron core.
3
Hysteresis Loss — Energy expended in repeatedly magnetizing and demagnetizing the core. Minimized by using soft iron, which has a small hysteresis loop.
4
Flux Leakage — Some magnetic flux from the primary doesn't link with the secondary. Minimized by efficient core design and winding techniques.

Efficiency ($eta$) is calculated as $\eta = \frac{P_{out}}{P_{in}} \times 100\%$. For NEET, practice numerical problems involving these formulas and conceptual questions on the types of losses and their minimization. For example, if a step-down transformer has $N_p=1000$, $N_s=100$, and $V_p=220,\text{V}$, then $V_s = 220 \times (100/1000) = 22,\text{V}$. If $I_p=1,\text{A}$ and $eta=90\%$, then $P_{in} = 220 \times 1 = 220,\text{W}$. $P_{out} = eta \times P_{in} = 0.90 \times 220 = 198,\text{W}$.

Prelims Revision Notes

Transformers are static devices for changing AC voltage/current levels via mutual induction. They do NOT work with DC. Key components: Primary coil ($N_p$ turns), Secondary coil ($N_s$ turns), Laminated soft iron core.

Ideal Transformer Equations:

Voltage Ratio: $\frac{V_s}{V_p} = \frac{N_s}{N_p} = k$ (Transformation Ratio)
Current Ratio: $\frac{I_s}{I_p} = \frac{N_p}{N_s} = \frac{1}{k}$
Power Conservation: $P_{in} = P_{out} \implies V_p I_p = V_s I_s$

Types of Transformers:

Step-up Transformer — $N_s > N_p \implies k > 1$. Increases voltage ($V_s > V_p$), decreases current ($I_s < I_p$). Used in power generation for transmission.
Step-down Transformer — $N_s < N_p \implies k < 1$. Decreases voltage ($V_s < V_p$), increases current ($I_s > I_p$). Used in substations and electronic devices.

Energy Losses in Real Transformers (and Minimization):

1
Copper Loss ($I^2R$ Loss) — Due to resistance of windings. Minimized by using thick copper wires (low resistance).
2
Eddy Current Loss — Induced circulating currents in the core. Minimized by using a laminated core (thin, insulated sheets).
3
Hysteresis Loss — Energy lost in magnetizing/demagnetizing the core. Minimized by using soft iron core (small hysteresis loop).
4
Flux Leakage — Magnetic flux from primary not linking secondary. Minimized by efficient core design and winding techniques.

Efficiency ($eta$):

$\eta = \frac{\text{Output Power}}{\text{Input Power}} \times 100\% = \frac{P_{out}}{P_{in}} \times 100\%$
Also, $P_{out} = P_{in} - P_{losses}$. So, $\eta = \frac{P_{in} - P_{losses}}{P_{in}} \times 100\%$.
For ideal transformer, $\eta = 100\%$.

Key Concepts for NEET:

Understand why AC is essential (changing flux).
Role of laminated soft iron core (reduce eddy currents, hysteresis, channel flux).
Direct application of voltage/current/turns ratios.
Calculations involving efficiency and various losses.
Distinguish between step-up and step-down characteristics.

Vyyuha Quick Recall

To remember transformer losses and their fixes: Can Every Heavy Fish Lose Some Weight?

Copper loss $\to$ Windings (thick wire)
Eddy current loss $\to$ Lamination (thin sheets)
Hysteresis loss $\to$ Soft iron (core material)
Flux Leakage $\to$ Winding design (coils over each other)