# Workings of a Transformer

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A transformer is a device that changes a high alternating voltage at low current to a low alternating voltage at high current or vice versa.

Structure of transformer:

• Primary coil: Connected to primary input voltage ($V_{p}$) with turns ($N_{p}$)
• Secondary coil: connected to load with output voltage ($V_{s}$) with turns ($N_{s}$)
• Soft-iron core: The coils are wound around a laminated soft-iron core, which consists of thin sheets of soft-iron insulated from one another. The lamination of the soft-iron core reduces the heat loss due to induced currents that could be formed in an otherwise unlaminated core.

A step-up transformer is one where the e.m.f. in the secondary coil is greater than the e.m.f. in the primary coil. A step-down transformer is one where the e.m.f. in the secondary coil is less than the e.m.f. in the primary coil.

Equation relating the voltage and number of turns:

$\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}$

Turns ratio: $\frac{N_{s}}{N_{p}}$

Power transfer in transformer: Power in primary coil = power in secondary coil

$I_{p}V_{p} = I_{s}V_{s}$

Problems and Improvements to transformer:

• Heat can be generated in the wires causing inefficiencies in transfer of electricity. Soln: Make the wires thick as this will reduce resistance $\rightarrow$ reduce heat generated
• Magnetic field lines can leak away so not all lines pass through the secondary coil. Soln: Use circular core
• Current induced in core can circle around heating up the core. Soln: Make core from thin laminated sheets. The lamination is to prevent loss of energy via heat that would otherwise be generated from the induced currents of an unlaminated core as currents cannot pass between the lamination.

Transmission of electrical power

During the transmission and distribution of electrical energy from the power station, there is power loss due to Joule heating, The power loss is given by:

$P_{L} = I^{2} R$

In order to reduce the power loss, we have to minimise I and R.

Very thick cables can be used to reduce the resistance R. However, the thick cables are heavy and expensive. Hence, the better option is to reduce I.

In order to reduce I, we can employ step-up transformers to increase the transmission voltage and reduce the current. This will reduce the energy loss due to Joule heating.

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