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Physics · 2024 · 2 marks
CBSE 2024 · Region 2 · Set 3 · Q24
An ac voltage v_i =140 sin (100 π t ) V is applied to the primary coil having 200 turns, of an ideal transformer and it supplies a power of 5 kW. If…
An ac voltage $\displaystyle \mathrm{v}_{\mathrm{i}}=140 \sin (100 \pi \mathrm{t}) \mathrm{V}$ is applied to the primary coil having $\displaystyle 200$ turns, of an ideal transformer and it supplies a power of $\displaystyle 5$ kW . If the secondary coil has $\displaystyle 1000$ turns, find :
(a)
the output voltage,
(b)
the instantaneous voltage across the secondary coil, and
(c)
the current in the secondary coil. (Take $\displaystyle \sqrt{2}=1 \cdot 4$ )
Marking-scheme solution
(a)
$\displaystyle V_{P(\mathrm{rms})}=\frac{140}{\sqrt{2}}=\frac{140}{1.4}=100 \mathrm{~V}$
$\displaystyle \therefore V_{s}=\frac{N_{s}}{N_{p}} V_{p}=\frac{1000}{200} \times 100=500 \mathrm{~V}$
(b)
$\displaystyle v_{s}=500 \sqrt{2} \sin 100 \pi t=700 \sin 100 \pi t$
(c)
Power output $\displaystyle =$ Power input
$\displaystyle I_{s}=\frac{5000}{500}=10 \mathrm{~A}$
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