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# In a transformer, the transformation ratio is 0.3. If $220 V$ ac is fed to the primary, then the voltage across the secondary will beA) $44V$B) $55V$C) $60V$D) $66V$

Last updated date: 21st Apr 2024
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Hint: The primary voltage and the transformation ratio is given in the question. The transformation ratio is the ratio of the secondary voltage to the primary. It is also the ratio of the number of turns in the secondary to the number of turns in the primary.

Formula used:
$\dfrac{{{V_S}}}{{{V_P}}} = \dfrac{{{N_S}}}{{{N_P}}}$ (Where, ${V_S}$ stands for the voltage in the secondary, ${V_P}$ stands for the voltage in the primary, ${N_S}$ stands for the number of turns in the secondary, and ${N_P}$ stands for the number of turns in the primary.

Complete step by step solution:
From the information given in the question, we have the voltage in the primary and the transformation ratio.
The primary voltage, ${V_P}$= $220V$
The transformation ratio is the ratio of secondary voltage to the primary voltage, it is also the ratio of the number of turns in the secondary to the number of turns in the primary.
In this question, for convenience, we take the transformation ratio as the ratio of the number of turns in the primary and secondary.
The transformation ratio, $\dfrac{{{N_S}}}{{{N_P}}}$= $0.3$
Now we have to find the voltage across the secondary coil, ${V_S}$
To find ${V_S}$ we use the formula $\dfrac{{{V_S}}}{{{V_P}}} = \dfrac{{{N_S}}}{{{N_P}}}$
From this equation, ${V_S} = \dfrac{{{N_S}}}{{{N_P}}} \times {V_P}$
The values are, ${V_P}$=$220V$ and $\dfrac{{{N_S}}}{{{N_P}}}$=$0.3$
Substituting these values in the equation
${V_S} = 0.3 \times 220$
${V_S} = 66$

The answer is option (D), $66V$.

Note: Here the voltage in the secondary is less than the voltage in the primary, this means that the transformer is a step-down transformer. In a step-up transformer, the voltage in the secondary will be greater than the voltage in the secondary. For a step-up transformer, the number of turns in the secondary will be greater than the number of turns in the primary. In a step-down transformer. The number of turns will be secondary and will be fewer than the number of turns in the primary.