alternating-currents Question 43
Question: Q. 10. (ii) Draw a schematic arrangement for winding of primary and secondary coil in a transformer when the two coils are wound on top of each other.
(ii) State the underlying principle of a transformer and obtain the expression for the ratio of secondary to primary voltage in terms of the
(a) number of secondary and primary windings and
(b) primary and secondary currents.
(iii) Write the main assumption involved in deriving the above relations.
(iv) Write any two reasons due to which energy losses may occur in actual transformers.
U [O.D. I, II, III 2014]
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Solution:
Ans.(i)
(ii) Principle of a transformer : When an alternatin current flows through the primary coil, an emf is induced in the neighbouring (secondarygeil/1/2 (a) Let $\frac{d \phi}{d t}$ be the rate of change of flux through each turn of the primary and the secondary coil
$$ \frac{\varepsilon_{1}}{\varepsilon_{2}}=\frac{-N_{1} \frac{d \phi}{d t}}{-N_{2} \frac{d \phi}{d t}}=\frac{N_{1}}{N_{2}} $$
or
$$ \begin{equation*} \frac{V_{1}}{V_{2}}=\frac{N_{1}}{N_{2}} \tag{i} \end{equation*} $$
(b) But for an ideal transformer,
$$ \begin{align*} & V_{1} I_{1}=V_{2} I_{2} \ & \frac{V_{1}}{V_{2}}=\frac{I_{2}}{I_{1}} \tag{ii} \end{align*} $$
From equation (i) and (ii)
$$ \frac{V_{1}}{V_{2}}=\frac{N_{1}}{N_{2}}=\frac{I_{2}}{I_{1}} $$
(iii) Main assumptions :
(a) The primary resistance and current are small. (b) The flux linked with the primary and secondary coils is same / there is no leakage of flux from the core.
(c) Secondary current is small.
$1 / 2$
(Any one)
(iv) Reason due to which energy losses may occur : Fluxleakage/Resistance of the coils/Eddy currents/ Hysteresis.
(Any two) $1 / 2+1 / 2$
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