Here we do a follow up on the Example $textbf{“Your Goose is cooked”}$ and we need to find out how long does goose have to be cooked if current and voltage are reduced by a factor of 2.

Reducing the current and voltage, we should calculate how much power is reduced, and then we can calculate the needed time. So the power is:

$$
P=I V
$$

Reducing it by a factor of 2 (and implementing the information from the problem statement in Goose Example):

$$
P=frac{20.0 mathrm{~A}}{2} cdot frac{220.0 mathrm{~V}}{2} \
$$

we get the result of:

$$
P=1.10 mathrm{~kW}
$$

With this power we need to deliver $17.6 mathrm{kWh}$ of energy, the time needed for that will be:

$$
Delta t =frac{Delta E} {P}
$$

Putting in the numbers, we have:

$$
Delta t =frac{17.6 times 10^{3} mathrm{Wh}} {1.1 times 10^{3} mathrm{W}}
$$

we have the result of:

$$
boxed{color{#c34632}Delta t =16 mathrm{h}}
$$

$$
Delta t =16 mathrm{h}
$$

Here we calculate how much does it cost to operate a lamp for an hour if it operates on 120 V and a current of 2.6 A and the cost of the energy is $$ 0.075$ $textbf{per kilowatt-hour}$.

First, since we know the current and voltage, we calculate how much power is consuming:

$$
P=VI
$$

Putting in the numbers we have:

$$
P=120 mathrm{V} cdot 2.6 mathrm{A}
$$

which gives the result of:

$$
P=312 mathrm{W}
$$

To get to know how much energy is consumed in an hour, first, we define the consumed energy:

$$
Delta Q = P Delta t
$$

And for 1 hour we got:

$$
Delta Q = 312 mathrm{W} 1 mathrm{h} = 312 mathrm{Wh}
$$

For our hourly rate of $$ 0.075$ $textbf{per kilowatt-hour}$ per hour it means 1000 Wh = $$ 0.075$, so the pirce will be:

$$
mathrm{PRICE} = $ 0.075 cdot frac{mathrm{Power}}{1000 mathrm{Wh}}
$$

Putting in the power we have:

$$
mathrm{PRICE} = $ 0.075 cdot frac{312 mathrm{W}}{1000 mathrm{Wh}}
$$

We get the result of:

$$
boxed{color{#c34632}mathrm{PRICE} = 0.0234 $}
$$

$$
mathrm{PRICE} = 0.0234 $
$$

Here we calculate the cost of electrical energy per kilowatt-hour on a specific location. We know it costs 2.6 cents on a 12 V battery and the current of 15 A for 120 min.

We calculate the cost of operating it per kilowatt-hour, which is literally how much is the cost of energy per hour. To get the energy, we will need power consumption.

Since we know voltage and current, we can calculate the power by multiplying them:

$$
P = UI
$$

Putting in the numbers we have:

$$
P = 12 mathrm{V} cdot 15 mathrm{A}
$$

We have the power of:

$$
P = 180 mathrm{W}
$$

To calculate the energy we use work-power relation and we take into account that 120 min = 2 hours:

$$
Delta E = P Delta t = 0.18 mathrm{kW} cdot 2 mathrm{hours} = 0.36 \mathrm{kWh}
$$

Now to get the cost per kWh we have:

$$
mathrm{COST} = frac{2.6 mathrm{cents}}{0.36 mathrm{kWh}}
$$

we have the result of:

$$
boxed{color{#c34632} mathrm{COST}=7.22 frac{mathrm{cents}}{mathrm{kWh}}}
$$

$$
mathrm{COST}= 7.22 frac{mathrm{cents}}{mathrm{kWh}}
$$