Talha's Physics Academy
Electromagnetic Induction - Transformers
Transformer: Definition and Construction
"A transformer is an electrical device that makes use of mutual induction for stepping up or stepping down an alternating emf."
Figure: Structure of a transformer with primary and secondary coils wound on a laminated soft iron core.
Construction
It consists of two coils of insulated copper wire—the primary coil and the secondary coil—wound either on top of each other or on separate limbs of a laminated soft iron core, linking them magnetically. The high permeability of the soft iron core ensures that virtually all magnetic flux generated by the primary coil passes through the secondary coil.
Working Principle
Suppose an alternating emf $E_p$ is applied to the primary coil. If at any instant the magnetic flux in the primary is $\Phi$, a back emf is induced in the primary according to Faraday's law:
$$E_p = -N_p \frac{\Delta \Phi}{\Delta t} \quad \text{--- (i)}$$
Assuming complete magnetic coupling, the magnetic flux passing through each turn of the secondary coil is the same as that in the primary. Thus, the induced emf $E_s$ in the secondary coil with $N_s$ turns is given by:
$E_s = -N_s \frac{\Delta \Phi}{\Delta t} \quad \text{--- (ii)}$
Dividing equation (ii) by equation (i), we obtain the transformation ratio:
$\frac{E_s}{E_p} = \frac{N_s}{N_p}$
- Step-Up Transformer: If $N_s > N_p$, then $E_s > E_p$, which increases the alternating voltage.
- Step-Down Transformer: If $N_s < N_p$, then $E_s < E_p$, which decreases the alternating voltage.
Transformer Efficiency
When a load (resistance) is connected across the secondary coil, an alternating current $I_s$ flows through the secondary, while $I_p$ flows through the primary. For an ideal transformer (100% efficient):
$$\text{Power Input} = \text{Power Output}$$
$$E_p I_p = E_s I_s \implies \frac{E_s}{E_p} = \frac{I_p}{I_s} = \frac{N_s}{N_p}$$
The efficiency ($\eta$) of a practical transformer is defined as the ratio of useful power output to the total power input, expressed as a percentage:
$\eta = \left( \frac{\text{Power Output}}{\text{Power Input}} \right) \times 100 = \left( \frac{E_s I_s}{E_p I_p} \right) \times 100$
Uses of Transformers
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Power Transmission:
Electric energy generated at power plants is transmitted over long distances using high voltages via step-up transformers. Because power loss in transmission lines is given by $P_{\text{loss}} = I^2 R$, raising the voltage drastically reduces the current $I$, minimizing $I^2 R$ heat losses. Step-down transformers are then used at substations to reduce the voltage to safe levels ($220\,\text{V} - 240\,\text{V}$) for residential and industrial use.
- Domestic Applications: Step-down transformers are used in homes to lower voltages from $220\,\text{V}$ to lower values (e.g., $4\,\text{V}$) for devices like doorbells.
- Electronic Appliances: Multi-secondary transformers are utilized in televisions, radios, and audio amplifiers to supply several distinct operating voltages.
Sources of Power Loss in Transformers
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1. Eddy Current Losses:
Changing magnetic flux induces circulating currents (eddy currents) within the iron core, causing thermal energy dissipation.
Minimization: The core is constructed from thin, laminated soft-iron sheets insulated from one another by varnish layers to restrict eddy current paths. -
2. Hysteresis Losses:
Continuous reversal of the magnetic field's direction inside the core expends energy overcoming molecular friction, generating heat.
Minimization: Specialized high-grade alloy materials (such as permalloy or silicon steel) are used for the core. -
3. Copper Losses ($I^2 R$ Loss):
Electric resistance in the primary and secondary copper windings causes ohmic heating ($I^2 R$).
Minimization: Coils carrying higher currents (fewer turns) are wound using thicker copper wire to lower resistance. -
4. Flux Leakage:
Not 100% of the magnetic flux generated by the primary coil links with the secondary coil due to imperfect magnetic coupling, resulting in slight energy loss.
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