The potential of a cloud is \( 4\times10^{6}\,\mathrm{V} \) with respect to the ground. In a lightning strike lasting 100 ms, a charge of 4 C is delivered to the ground. The power of the lightning strike is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 160 MW
When a charge \( Q \) moves through a potential difference \( V \), the energy delivered is \( W=QV \). The power is this energy divided by the time it takes.
\( \begin{aligned} W &= QV \\ &= 4\,\mathrm{C}\times4\times10^{6}\,\mathrm{V} \\ &= 1.6\times10^{7}\,\mathrm{J} \end{aligned} \)
\( t=100\,\mathrm{ms}=0.1\,\mathrm{s} \)
\( \begin{aligned} P &= \frac{W}{t} \\ &= \frac{1.6\times10^{7}\,\mathrm{J}}{0.1\,\mathrm{s}} \\ &= 1.6\times10^{8}\,\mathrm{W} \\ &= 160\,\mathrm{MW} \end{aligned} \)