A generator gives 10 kW of power at 200 V. An ideal transformer steps this voltage up to 2000 V. The power is then sent through transmission lines of total resistance 2 Ω. The power lost as heat in the lines is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(50\ \mathrm{W}\)
An ideal transformer passes on the whole power. At the higher voltage, the same power needs a smaller current, \( I=P/V \). The heat lost in the lines is \( I^{2}R \).
Given:
\( P=10\ \mathrm{kW}=10^{4}\ \mathrm{W} \)
\( V=2000\ \mathrm{V} \)
\( R=2\ \Omega \)
\( \begin{aligned} I &= \frac{P}{V} \\ &= \frac{10^{4}}{2000} \\ &= 5\ \mathrm{A} \end{aligned} \)
\( \begin{aligned} P_{\mathrm{loss}} &= I^{2}R \\ &= 5^{2}\times2 \\ &= 50\ \mathrm{W} \end{aligned} \)
NCERT (2026-27):
Transformers – “The large scale transmission and distribution of electrical energy over long distances is done with the use of transformers. The voltage output of the generator is stepped-up (so that current is reduced and consequently, the I2R loss is cut down). …”