How Much Does It Cost to Run a Digital Clock for 34 Days?

[haleyscavone]

A digital clock has an operating resistance of 11000 and is plugged into a 114-V outlet. Assume the clock obeys Ohm's law.

If the owner of the clock pays $0.09 per kWh, what does it cost to operate the clock for 34 days?

Where do I even begin?

 

[Borek]

What current goes through the clock?

How does power depend on the current and voltage?

 

[thomate1]

Well, first of all, let's break down the information we have. We know that the digital clock has an operating resistance of 11000 ohms and is plugged into a 114-V outlet. This means that the current flowing through the clock is 114/11000 = 0.01036 amperes (according to Ohm's law, I = V/R).

Now, to convert this current into kilowatt-hours (kWh), we need to multiply it by the time the clock is in operation. In this case, we are given the time frame of 34 days. So, we first need to convert 34 days into hours, which is 34 x 24 = 816 hours.

Next, we need to convert amperes to kilowatts (kW) by dividing the current by 1000. So, 0.01036 amperes is equal to 0.01036 / 1000 = 0.00001036 kW.

Finally, to get the total energy consumption in kWh, we multiply the kW by the number of hours the clock was in operation. So, 0.00001036 kW x 816 hours = 0.00845 kWh.

Now, to find the cost, we simply multiply the energy consumption (in kWh) by the cost per kWh. In this case, the cost is $0.09 per kWh, so the total cost to operate the clock for 34 days is 0.00845 kWh x $0.09 = $0.0007615.

In summary, to find the cost of operating the digital clock for 34 days, we first converted the current into kWh by multiplying it by the time in operation. Then, we multiplied the kWh by the cost per kWh to get the total cost.