Answer:
a) 15 C charge was delivered by the lightening bolt
b) the lightning delivered 3.0 × 10¹² W of power
c)
- total energy delivered by the lightening strike in J is 1500 × 10⁶ J
- total energy delivered by the lightening strike in Wh is 416666.67 Wh
d)
the residential retail value of the energy delivered by the strike is $ 40.83
e)
a total of 26 lightening strikes would be required to power an average US home for a year.
Explanation:
Given that;
the lighting strike lasted for t ( time ) = 500 μsecs = 500×10⁻⁶ s
Current I = 30 kA = 30×10³ A
voltage V = 100 mV = 100×10⁶ v
a)
we know that; I = Q/t
so Q = I × t
we substitute
Q = 30×10³ × 500×10⁻⁶
Q = 15 C
Therefore 15 C charge was delivered by the lightening bolt
b)
Power P = V × I
we substitute
Power P = 100×10⁶ × 30×10³
P = 3.0 × 10¹² W
Therefore, the lightning delivered 3.0 × 10¹² W of power
c)
we know that; Power = Energy / Time
Energy = Power × Time
we substitute
E = 3.0 × 10¹² × 500×10⁻⁶
E = 1500 × 10⁶ J
- total energy delivered by the lightening strike in J is 1500 × 10⁶ J
- total energy delivered by the lightening strike in Wh is;
⇒ 1500×10⁶ / 3600 Wh
= 416666.67 Wh
d)
given that; 1 KWh → $ 0.098
energy delivered by the strike = 416666.67 Wh = 416.66667 KWh
so the residential retail value of the energy delivered by the strike will be;
416.66667 KWh × $ 0.098
= $ 40.83
∴ the residential retail value of the energy delivered by the strike is $ 40.83
e)
Given that; average monthly residential energy consumption is 900 kWh.
for a year; energy consumption = 12 × 900 kWh = 10,800 KWh = 10800000 Wh
Now
1 lightening strike ⇒ 416666.67 Wh
x lightening strike ⇒ 10800000 Wh
x = 10800000 / 416666.67
x = 25.9199 ≈ 26
Therefore; a total of 26 lightening strikes would be required to power an average US home for a year.
