Problems - Single Capacitors P19-1. If 9 V is maintained across a 200 muF capaci

Question

Problems - Single Capacitors P19-1. If 9 V is maintained across a 200 muF capacitor, how much energy is stored? P19-2. If a lightning strike can be approximated by considering a cloud and the Earth as a parallel plate capacitor, A) find the capacitance of such a system if the cloud's dimensions are 8 km by 9km, at a height of 600 m. B) If 50 C of charge sit on the cloud, find the energy stored in this system. P19-3. A hazard warning flasher consists of a light bulb and a 500 muF capacitor. When the bulb lights up, 40 J of energy to converted to light and heat. A) What voltage must be applied across the capacitor? B) What is the capacitor's initial charge?

Explanation / Answer

1)

Energy stored = 0.5*C*V^2 = 0.5*(200*10^-6)*9^2 = 0.0081 J

2)

Capacitance, C = eA/d

where e = permittivity of air = 8.854*10^-12

A = area = 8km*9km = 72 km2 = 72*10^6 m2

d = 600 m

So, C = 8.854*10^-12*(72*10^6/600) = 1.06*10^-6 F <--------answer

B)

Energy stored = Q^2/2C = 30^2/(2*1.06*10^-6) = 4.25*10^8 J <--------answer

3)

A)

E = 0.5*C*V^2

So, 40 = 0.5*(500*10^-6)*V^2

So, V = 400 V <----answer

B)

Charge = C*V = 500*10^-6*400 = 0.2 F <----answer

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