Question

The voltage of clouds is $4 \times {10^6}$ volt with respect to a lightning strike lasting 100 millisec, a charge of 4 coulomb is delivered to the ground. The power of the lightning strike is:

A) 160 MW
B) 20 MW
C) 80 MW
D) 500 MW

Answer 1

To solve this particular question one must have a clear idea about the concept of potential difference, work done and power. In other words, the potential difference between two points or terminals is the work required in Joules to move one Coulomb of charge. This definition along with the definition of power is the key to solve this question.

Complete step by step answer: Given, Voltage (V) = $4 \times {10^6}$ volt; Charge (Q) = 4 C; time (t) = 100 millisec = 0.1 sec
We know that the voltage or potential difference between two points is nothing but the amount of work required to move a unit charge from one point to another. Hence, mathematically we can write that,
$V = \dfrac{W}{Q}$
Therefore work done can be obtained from the following equation,
$W = V \times Q = 4 \times {10^6} \times 4$
$W = 16 \times {10^6}J$………….(1)
Now, power is the rate of change of work with respect to time (i.e work done per unit time). Hence, the power of the lightning strike can be calculated by the following equation.
$P = \dfrac{W}{t}$
Putting the value of work done (W) from equation (1) in the above equation, we get the power of lightning strike,
$P = \dfrac{{16 \times {{10}^6}}}{{0.1}} = 160 \times {10^6}$
$P = 160MW$
Hence, the power of the lightning strike is 160 MW.

Therefore, answer option A is the correct choice.

Note:
-The unit of power is watt (W), 1 W = 1 J/s.
-One volt of potential difference is obtained when 1 joule of work is done on a charge of one coulomb $1Volt = \dfrac{{1Joule}}{{1Coulomb}}$ , i.e 1V= 1 J/C
-An electric spark in the atmosphere is known as lightning.
-When lightning strikes the earth it fuses dirt and clay to form silica.