Subject: Physics
The transformer is a device used to convert low alternating voltage at high current into the high alternating voltage at low current and vice versa. The transformer is an electrical device used to increase or decrease alternating voltage.
There are two types of transformers. They are:
It is based on the principle of mutual induction i.e. when the magnetic flux linked with a coil is changed, e.m.f. is induced in the nearby coil.
It consists of two windings or coils, the primary and secondary, wound on common laminated soft-iron core. The coil connected to the a.c. the source is called primary coil and the coil connected to the load is called secondary coil. The primary coil along with load is called primary circuit and the secondary coil along with load is called secondary circuit.
When an a.c. source of e.m.f Ep is connected to the primary coil, an alternating current flows through it so that alternating magnetic field is produced and hence magnetic flux linked with the coil and Ns be the number of turns in the primary and secondary coils respectively. The iron coil is capable of coupling all of the magnetic flux \(\phi \) produced by the turns of the primary coil with the secondary coil.
\begin{align*} \epsilon_p &= -N_p\frac {d\phi }{dt} \dots (i) \\ \text {The induced e.m.f. in the secondary coil,} \\ \epsilon_s &= N_s \frac {d\phi }{dt} \dots (ii)\\ \text {Dividing equation}\: (ii)\:\text {by}\:(i), \: \text {we get}\\ \frac {\epsilon _s}{\epsilon _p} &= \frac {N_s}{N_p} \\ \end{align*}
\begin{align*} \text {where}\: \frac {N_s}{N_p} &= \sqrt {\frac {L_P}{L_S}} = k \: \text {transformation ratio.} \\ \text {Here,}\\ L_P &= \text {coefficient of self induction of primary coil} \\ L_S &= \text {coefficient of self induction of secondary coil} \\ \therefore {\epsilon _s}{\epsilon _p} &= \frac {N_s}{N_p} = K \dots (iii) \\\end{align*}
\begin{align*} \text {For step-down transformer,} \: K< 1\\ \text {For step-up transformer} \: K >1 \\ \text {For an ideal transformer} \\ \text {Output power} &= \text {Input power} \\ \text {or,} \: {\epsilon _s}{\epsilon _p} &= \frac {I_p}{I_s} \dots (iv) \\ \text {In general,}\: \epsilon \propto \frac 1I \\ \end{align*}
A step-up transformer increases the alternating voltage by decreasing the alternating current and a step-down transformer decreases the alternating voltage by increasing the alternating current.
For a transformer,
\begin{align*}\text {efficiency,}\: \eta &= \frac {\text {output power}}{\text {input power}} = \frac {E_SI_S}{E_PE_P} \\ \end{align*}
Reference
Manu Kumar Khatry, Manoj Kumar Thapa, Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.
S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.
Transformer is a device used to convert low alternating voltage at high current into high alternating voltage at low current and vice versa.
Energy lost in windings of the transformer is known as copper loss.
A step-up transformer increases the alternating voltage by decreasing the alternating current and a step-down transformer decreases the alternating voltage by increasing the alternating current.
For a transformer,
\begin{align*}\text {efficiency,}\: \eta &= \frac {\text {output power}}{\text {input power}} = \frac {E_SI_S}{E_PE_P} \\ \end{align*}
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