How much energy is imparted by the lightning strike how

Question

WARM-UP PROBLEMS

 

1) We will oft dad with find voltage and current in this course, but it's important to remember that charger, current and voltage can each be a time-varying function. Determine the current i(t) flowing through a resistor if the charge flow q(t) it defined as:

 

a- q(t) = 7C

 

b- q(t) = (3t +8)m

 

c- q(t) = 0.3 (1 - e^-0.4t) pC

 

2) Consider a battery-powered LED flashlight that draws 100 mA when 'witched on:

 

a. If this operates for 3h, how much charge is &triad?

 

b. If this is driven by a 9V battery (during the 3h), how much emir is used?

 

c. How much power is consumed while the flashlight is switched on

 

3) The current through an electrical device is given as i(t) = 30e^-0.2t mA, and the voltage through the device is given as v(t) =  100( 1 - e^-0.2t) Y. For this, device, determine:

 

a. The charge delivered from t =0 to t = 3s.

 

b. The instantaneous power at t = 2s.

 

c. The total energy delivered for all time (ie. from t = 0 to t = ∞).

 

APPLIED PROBLEMS

 

1. Yon should now be comfortable with charge, current, voltage, power, sad energy. A 12kA lightning bolt snags in object for is 15 μs. Consider the following:

 

a. How much charge is deposited on the object?

 

b. How many electrons is this?

 

c. If the lightning strike discharges across a voltage potential of 250 million volts, what is the lightning bolt's power?

 

d. How much energy is imparted by the lightning strike?

 

e. A typical cell phone battery has a charged capacity of 1800 mAh at 3.7 V. If the energy front the lightning strike  were harnessed, how many cell phone batteries could be fully charged using this energy?

 

2) Electric power is often used to generate heat. You might use an electric kettle to heat up 12 ounces of water for a mug of tea. Water has a very high heat capacity, so this uses a lot of energy. We can use the specific heat of water (c_water = 4186 J/kg ^oC) to calculate the total energy I required to heat the water: E = cmΔT, where c is specific heat, m is the mass of water, and Al is the change in temperature. Assume that the water starts at room temperature (25^oC).

 

a. How much energy (in joules) is required to heat the water to boiling (MM.)?

 

b. If the price for electricity is 10.78 ¢ /kWh from Pacific Power in Oregon, how many mugs of tea can you make for $1? (Assume that water and tea arc free, and assume that the water absorbs all of the electric power delivered. Note: These are generally unsafe assumptions.)

 

c. Your electric kettle operates at a constant current of 15A and a constant voltage of 120V.

 

i. How much energy does it consume in five minutes of continuous operation?

 

ii. How many mugs of tea can this heat?

 

iii. How much would this energy cost using the Pacific Power rate in 2b?