Question

An electric heater draws a steady 15.0A on a 120-V
line. How much power does it require and how
much does it cost per month (31days) if it operates
2.0 h per day and the electric company charges 15.5
cents per kWh?

Answer 1

Answer:

1. 1800 W

2. $ 17.3

Explanation:

From the question given above, the following data were obtained:

Current (I) = 15 A

Voltage (V) = 120 V

Time (t) = 20 h per day

Duration = 31 days

Cost = 15.5 cents per kWh

1. Determination of the power.

Current (I) = 15 A

Voltage (V) = 120 V

Power (P) =?

P = IV

P = 15 × 120

P = 1800 W

Thus, 1800 W of power is required.

2. Determination of the cost per month (31 days).

We'll begin by converting 1800 W to KW.

1000 W = 1 KW

Therefore,

1800 W = 1800 W × 1 KW / 1000 W

1800 W = 1.8 KW

Next, we shall determine the energy consumption for 31 days. This can be obtained as follow:

Power (P) = 1.8 KW

Time (t) = 2 h per day

Time (t) for 31 days = 2 × 31 = 62 h

Energy (E) =?

E = Pt

E = 1.8 × 62

E = 111.6 KWh

Finally, we shall determine the cost of consumption. This can be obtained as follow:

1 KWh = 15.5 cents

Therefore,

111.6 KWh = 111.6 KWh × 15.5 cents / 1 KWh

111.6 KWh = 1729.8 cents

Converting 1729.8 cents to dollar, we have:

100 cents = $ 1

Therefore,

1729.8 cents = 1729.8 cents × $ 1 / 100 cents

1729.8 cents = $ 17.3

Thus, it will cost $ 17.3 per month to run the electric heater.

Answer 2

The amount of power it requires is 180 Watt, and the cost per month to operate the electric heater for 2.0 h is 5.58 cent

To calculate the electric power required by the electric heater, we use the formula below.

⇒ Formula:

• P = Vi................ Equation 1

⇒ Where:

• P = Power
• V = Voltage
• i = current

From the question,

⇒ Given:

• V = 120 V
• I = 15.0 A

⇒ Substitute these values into equation 1

• P = 120(1.5)
• P = 180 Watt.

For the cost of running the electric heater per month, if it operates 2.0 h per day. We use the relation below

• C = Pt×C'/1000............... Equation 2

⇒ Where:

• C = The cost per month to operate the electric heater for 2.0h
• t = time
• C' = Cost per kWh charge by the electric company.

From the question,

⇒ Given:

• C' = 15.5 cent per kWh
• t = 2.0 h
• P = 180 Watt

⇒ Substitute these values into equation 2

• C = 180(15.5)(2)/1000
• C = 5.58 cent.

Hence, The amount of power it requires is 180 Watt, and the cost per month to operate the electric heater for 2.0h is 5.58 cent

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