Question

An electric furnace runs 13 hours a day to heat a house during January (31 days). The heating element has a resistance of 7.2 and carries a current of 16.7 A. The cost of electricity is $0.10/kWh. Find the cost of running the furnace during January.

Answer 1

$ 80.9

Step-by-step explanation:

Resistance, R = 7.2 ohm

current, i = 16.7 A

Cost = $ 0.10 / kWh

time = 13 hours per day , 1 month

Energy = i²Rt

E = 16.7 x 16.7 x 7.2 x 13 x 31 Wh

E = 809.28 kWh

Cost of 1 kWh = $ 0.10

Cost of 809.28 = $ 0.10 x 809.28 = $ 80.9

Answer 2

cost of running the furnace during January is $5619.62

Step-by-step explanation:

given data

runs a day = 13 hours

January days = 31 days

resistance = 7.2 ohm

current = 16.7 A

cost of electricity = $0.10/kWh

to find out

cost of running the furnace during January

solution

first we get her power consumed by furnace that is

Power consumed =
`(I^2)/(R)` ........1

put here value we get

Power consumed =
`(16.7^2)/(7.2)`

Power consumed = 38.7347 W

and

Power consumed by furnace in one hour is

Power consumed by furnace in one hour is = Power consumed × 3600

Power consumed by furnace in one hour is = 38.7347 × 3600

Power consumed by furnace in one hour is 139.445kWh

and

Power consumed by furnace in the month of January is

Power consumed by furnace in the month of January = 139.445kWh × 13 hours × 31 days

Power consumed by furnace in the month of January = 56196.335 kWh

so

cost of running the furnace during January is = $0.10/kWh × 56196.335 kWh

cost of running the furnace during January is $5619.62