A transistor radio operates by means of a 9.0 V battery that supplies it with a 40 mA current.

(a) If the cost of the battery is $0.50 and it lasts for 300 h, what is the cost per kWh to operate the radio in this manner?
(b) The same radio, by means of a converter, is plugged into a household circuit by a homeowner who pays 7 cent per kWh. What does it now cost to operate the radio for 300 h?

a. 9*0.04*300/1000 = 0.108kWh.

C = 0.50/0.108 = $4.63/kWh.

b. C = 0.07/kWh * 0.108kWh = $0.00756

To find the cost per kWh to operate the transistor radio, we need to first calculate the energy consumed by the radio in kilowatt-hours (kWh).

(a) Energy consumed by the transistor radio:
Since the radio operates at 9.0 V and draws a current of 40 mA, we can use Ohm's Law (V = I * R) to find the resistance (R) of the radio.
R = V / I
R = 9.0 V / 0.040 A
R = 225 Ω (ohms)

Next, we can calculate the power (P) consumed by the radio using the formula P = I * V:
P = 0.040 A * 9.0 V
P = 0.36 W (watts)

The energy consumed by the radio in 300 hours is given by the formula E = P * t:
E = 0.36 W * 300 h
E = 108 Wh (watt-hours)

To convert watt-hours to kilowatt-hours, we divide by 1000:
E = 108 Wh / 1000
E = 0.108 kWh (kilowatt-hours)

Now we can calculate the cost per kWh:
The cost of the battery is given as $0.50 and it lasts for 300 h. Therefore, the cost per hour is $0.50 / 300 = $0.0017 (rounded to four decimal places).

To find the cost per kWh, we can divide the cost per hour by the energy consumption in kWh:
Cost per kWh = Cost per hour / Energy in kWh
Cost per kWh = $0.0017 / 0.108 kWh
Cost per kWh ≈ $0.0157 (rounded to four decimal places)

Therefore, the cost per kWh to operate the radio using the battery is approximately $0.0157.

(b) To calculate the cost of operating the radio for 300 hours when plugged into a household circuit at a rate of 7 cents per kWh, we simply multiply the energy consumption by the rate:

Cost = Energy in kWh * Rate
Cost = 0.108 kWh * $0.07/kWh
Cost ≈ $0.00756 (rounded to two decimal places)

Therefore, it would cost approximately $0.00756 to operate the radio for 300 hours when plugged into a household circuit at a rate of 7 cents per kWh.

To calculate the cost per kWh to operate the radio, we need to determine the energy consumption in kWh first.

(a) Energy consumption:
The power consumed by the radio can be calculated using the formula: P = IV, where P is power in watts, I is current in amperes, and V is voltage in volts.
Given:
I = 40 mA = 0.04 A
V = 9.0 V

P = IV = 0.04 A * 9.0 V = 0.36 W

To determine the energy consumed in kWh, we need to convert the time in hours:
t = 300 hours

Energy = P * t = 0.36 W * 300 h = 108 Wh = 0.108 kWh

The cost per kWh is given as $0.50.
Therefore, the cost to operate the radio in this manner is:

Cost = Energy * Cost per kWh = 0.108 kWh * $0.50 = $0.054

So, the cost per kWh to operate the radio is $0.054.

(b) If the homeowner pays 7 cents per kWh, we can calculate the cost to operate the radio for 300 hours using the new cost per kWh.

Cost per kWh = $0.07

Cost = Energy * Cost per kWh = 0.108 kWh * $0.07 = $0.00756

Therefore, it now costs $0.00756 to operate the radio for 300 hours when plugged into a household circuit.