ANAND CLASSES Study Material and Notes to Master the concept of the commercial unit of electrical energy (kilowatt-hour) and derive the Relation between kilowatt-hour and joule with CBSE Class 10 Science notes, solved numericals, FAQs, MCQs with answers, assertion-reason questions, and a printable worksheet. Perfect for board exam preparation.

⚡ Calculating Electrical Energy

We will now derive a formula for calculating electrical energy in terms of power and time. We have already studied that :

$$\text{Electric Power} = \frac{\text{Work done by electric current}}{\text{Time taken}} $$

Now, according to the law of conservation of energy, Work done by electric current = Electric energy consumed.

So, we can now write down the above relation as :

$$\text{Power} = \frac{\text{Electrical Energy}}{\text{Time}} $$

$$ \text{Electrical Energy} = \text{Power} \times \text{Time}$$

or $$E = P \times t$$

Hence the electrical energy consumed by an electrical appliance is given by the product of its power rating and the time for which it is used.

From this we conclude that the electrical energy consumed by an electrical appliance depends on two factors :

(i) power rating of the appliance, and

(ii) time for which the appliance is used

🔁 SI Units:

If:

• P in watts
• t in hours
• Then, E is in watt-hour (Wh)

One Watt-hour (Wh) is the energy consumed by 1 W device in 1 hour.

🔌 Commercial Unit of Electrical Energy: Kilowatt-Hour (kWh)

The SI unit of electrical energy is the joule (J). By definition:

1 joule is the energy consumed when an appliance of 1 watt power is used for 1 second.

However, the joule is a very small unit and is inconvenient for practical, large-scale energy measurements—such as those in households and industries. Hence, we use a larger unit known as the:

⚡ Kilowatt-Hour (kWh)

One kilowatt-hour is the amount of electrical energy consumed when an electrical appliance having a power rating of 1 kilowatt is used for 1 hour.

Since a kilowatt means 1000 watts, so we can also say that one kilowatt-hour is the amount of electrical energy consumed when an electrical appliance of 1000 watts is used for 1 hour. In other words, one kilowatt-hour is the energy dissipated by a current at the rate of 1000 watts for 1 hour.

From this discussion we conclude that the commercial unit of electrical energy is kilowatt-hour which is written in short form as kWh.

📘 Relation between kilowatt-hour and joule

What is 1 Kilowatt-Hour?

1 kilowatt-hour is the electrical energy consumed when an appliance with a power rating of 1 kilowatt (kW) is used for 1 hour.

• Since 1 kilowatt = 1000 watts
• And 1 hour = 3600 seconds

We can express this as :

$$E = P \times t$$

1 kWh = 1000 watts × 3600 seconds = 3.6 × 10⁶ joules

👉 So,

$\boxed{1 \text{ kWh} = 3.6 \times 10^6 \, \text{J}}$

📝 Note:

• Watt or kilowatt is the unit of power
• Kilowatt-hour is the unit of energy

🧠 Numerical Problems

Q: A radio set of 60 watts runs for 50 hours. How much energy is consumed?

Solution:

Convert watts to kilowatts : P = 60/1000=0.06 kW

Time, t = 50 hours

Then, E = P × t = 0.06 × 50 = 3 kWh

Q: A current of 4 A flows through a 12 V bulb for 10 minutes. What is the energy transfer?

Solution:

Power : P = V × I = 12 × 4 = 48 W = 0.048 kW

Time: t = 10/60=1/6 hour

Energy : E = 0.048 × 1/6 = 0.008 kWh

Q: A 5 A current flows through a 2-ohm resistor for 30 minutes. Calculate the energy transferred.

Solution:

Using P = I²R :

P = 5² × 2 = 25 × 2 = 50 W = 50/1000 = 0.05 kW

Time: t = 30/60 = 0.5 hour

Then, E = 0.05 × 0.5 = 0.025 kWh

👉 You can convert this to joules: E = 0.025 × 3.6×10⁶ = 9 × 10⁴ J

💰 How to Calculate the Cost of Electrical Energy Consumed (Calculating Electricity Bill) ?

Kilowatt-hour is the “unit” of electrical energy for which we pay to the Electricity Supply Department of our City.

The energy used at home is measured in kWh, which is also called “unit” of electricity.

If:

• 1 unit = 1 kWh
• Cost of 1 unit = ₹3.40 (for example)

Then to calculate total cost :

Total Cost = Units Consumed × Rate per Unit

🧪 Example: Monthly Energy Cost

Q: A refrigerator having a power rating of 350 W operates for 10 hours a day. Calculate the cost of electrical energy to operate it for a month of 30 days. The rate of electrical energy is ₹3.40 per kWh.

Solution : A 350 W refrigerator runs 10 hours/day for 30 days. Our aim is yo calculate the cost at ₹3.40 per unit.

Power : P = 350/1000 = 0.35 kW

Time : t = 10 × 30 = 300 hours

Energy : E = 0.35 × 300 = 105 kWh

Cost : Total Cost = 105 × 3.40 = ₹357

🧮 Example: Bulb Consumption and Cost

Q: A bulb is rated at 200 V-100 W. What is its resistance ? Five such bulbs burn for 4 hours. What is the electrical energy consumed ? Calculate the cost if the rate is ₹4.60 per unit.

Solution : Convert Power to kW:

P = 100/1000 = 0.1 kW

Energy/day for each bulb : E = P x t

E = 0.1 × 4 = 0.4 kWh

Energy/day for 5 such bulbs :

E = 0.4 × 5 = 2 kWh = 2 units

Thus, the total electrical energy consumed is “2 kilowatt-hours” or “2 units”.

Total Cost :

Cost of 1 unit of electricity = ₹4.60

Total Cost = Units Consumed x Cost/Unit

Total Cost = 2 × 4.60 = ₹9.20

🔥 Example: Heater Usage Cost

Q: An electric heater draws a current of 10 A from a 220 V supply. What is the cost of using the heater for 5 hours everyday for 30 days if the cost of 1 unit (1 kWh) is ₹5.20 ?

Power Consumed : First of all we have to calculate the power of the heater by using the given values of current and voltage. This can be done by using the formula :

P = V × I

P = 220 × 10 = 2200 W = 2.2 kW

Electric energy consumed in 1 day :

E = P × t

E = 2.2 kW × 5h = 11 kWh

Electric energy consumed in 30 days :

E = 11 x 30 = 330 kWh = 330 units

Total Cost :

Cost of 1 unit of electricity = ₹5.20

Cost of 330 units of electricity = 330 × 5.20 = ₹1716

🔍 Frequently Asked Questions (FAQs)

❓ Q1: What is the SI unit of electrical energy?

Answer:
The SI unit of electrical energy is joule (J).

❓ Q2: Why is joule not used as a commercial unit of electrical energy?

Answer:
A joule is a very small unit of energy. In practical and commercial applications, large amounts of electrical energy are used, so using joules becomes inconvenient. Hence, a larger unit like kilowatt-hour (kWh) is used commercially.

❓ Q3: What is one kilowatt-hour (1 kWh)?

Answer:
One kilowatt-hour is the amount of electrical energy consumed when an appliance of 1 kilowatt (1000 watts) is used for 1 hour.

❓ Q4: What is the relation between kilowatt-hour and joule?

Answer: 1 kWh = 1000 W × 3600 s = 3.6×10⁶ J

❓ Q5: Is kilowatt-hour a unit of power or energy?

Answer:
Kilowatt-hour is a unit of energy, not power. Power is measured in watts or kilowatts.

❓ Q6: What is the formula to calculate electrical energy?

Answer:
Electrical energy is given by: E = P × t

where

• E = energy in kilowatt-hours (kWh)
• P = power in kilowatts (kW)
• t = time in hours (h)

❓ Q7: What do we mean by “1 unit” of electricity?

Answer:
One unit of electricity refers to 1 kilowatt-hour (kWh) of electrical energy.

🧠 Conceptual Questions with Answers

💡 Q1: If a device consumes 2 kWh in 1 hour, what is its power rating?

Answer:
Using E = P × t, we get:

$$P = \frac{E}{t} = \frac{2 \text{ kWh}}{1 \text{ h}} = 2 \text{ kW}$$

So, the power rating is 2 kilowatts.

💡 Q2: A fan rated at 120 W runs for 5 hours daily. How much energy is consumed in a week in kWh?

Answer:
Convert 120 W to kW: P = 120/1000=0.12 kW

Time in a week = 5 × 7 = 35 hours

Using E = P × t, we get:
Energy consumed, E = 0.12 × 35 = 4.2 kWh

💡 Q3: A 500 W heater is used for 2 hours daily for 30 days. Calculate the cost if 1 unit costs ₹5.

Answer:

Convert 500 W to kW : P=0.5 kW, t = 2 × 30 = 60 h

Energy consumed : E = P x t

E= 0.5 × 60 = 30 kWh

Total Cost: 30 × 5 = ₹150

💡 Q4: Can a 60 W bulb and a 100 W bulb running for 10 hours consume the same energy?

Answer:
No. The 100 W bulb will consume more energy.
Energy consumed = P × t

• For 60 W:
  60/1000 × 10 = 0.6 kWh
• For 100 W:
  100/1000 × 10 = 1.0 kWh

💡 Q5: A geyser consumes 4.5 kWh in 3 hours. What is its power?

Answer: P = E/t = 4.5/3 = 1.5 kW

So, the geyser’s power is 1.5 kilowatts.

Here’s a set of MCQs with explanations on the topic Commercial Unit of Electrical Energy – Kilowatt-Hour (kWh) for Class 10 Science. The math is MathJax-compatible using $$...$$.

✅ Multiple Choice Questions (MCQs) with Answers and Explanations

🔹 Q1. The commercial unit of electrical energy is:

A. Joule
B. Watt
C. Kilowatt-hour
D. Kilowatt

Answer: ✅ C. Kilowatt-hour
Explanation:
Though the SI unit of energy is the joule, for large-scale electricity billing and commercial use, energy is measured in kilowatt-hours (kWh).

🔹 Q2. 1 kilowatt-hour is equal to how many joules?

A. 3.6×10⁵ J
B. 3.6×10⁶ J
C. 3.6×10⁴ J
D. 3.6×10³ J

Answer: ✅ B. 3.6×10⁶ J
Explanation: 1 kWh = 1000 W × 3600 s = 3.6×10⁶ J

🔹 Q3. If a 100 W bulb is used for 10 hours, how much energy is consumed?

A. 1 kWh
B. 0.1 kWh
C. 0.5 kWh
D. 2 kWh

Answer: ✅ A. 1 kWh
Explanation:
Convert 100 W to kW: 100/1000=0.1 kW\frac{100}{1000} = 0.1 \text{ kW}

Then, E = 0.1 × 10 = 1 kWh

🔹 Q4. An appliance rated 2 kW runs for 3 hours. What is the energy consumed?

A. 6 kWh
B. 2 kWh
C. 5 kWh
D. 1.5 kWh

Answer: ✅ A. 6 kWh
Explanation:
Using the formula: E = P × t = 2 × 3 = 6 kWh

🔹 Q5. What will be the cost of using a 1.5 kW geyser for 4 hours if 1 unit costs ₹6?

A. ₹24
B. ₹36
C. ₹12
D. ₹30

Answer: ✅ B. ₹36
Explanation: E = 1.5 × 4 = 6 kWh

Cost = 6 × 6 = ₹36

🔹 Q6. Which of the following is NOT a unit of energy?

A. Joule
B. Kilowatt-hour
C. Watt
D. Calorie

Answer: ✅ C. Watt
Explanation:

• Joule, kilowatt-hour, and calorie are units of energy.
• Watt is a unit of power.

🔹 Q7. A refrigerator consumes 1.2 kWh per day. What is the total energy used in 30 days?

A. 36 kWh
B. 60 kWh
C. 120 kWh
D. 180 kWh

Answer: ✅ A. 36 kWh
Explanation: 1.2 × 30 = 36 kWh

🔹 Q8. A 500 W iron is used for 2 hours per day. How many units are consumed in 10 days?

A. 5 kWh
B. 10 kWh
C. 1 kWh
D. 2.5 kWh

Answer: ✅ B. 10 kWh
Explanation:
Convert 500 W to kW: 0.5 kW, t =2 × 10 = 20 hours

Energy consumed: 0.5 × 20 = 10 kWh

The right answer is ✅ B. 10 kWh

✅ Assertion and Reason Type Questions

Instructions:

• A: Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
• B: Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.
• C: Assertion is true, but Reason is false.
• D: Assertion is false, but Reason is true.

🔹 Q1.

Assertion: The commercial unit of electrical energy is kilowatt-hour (kWh).
Reason: 1 kilowatt-hour = 3.6×10⁶ joules.

Answer: ✅ A
Explanation:
Both the assertion and reason are true, and the reason correctly explains why kilowatt-hour is a valid energy unit used commercially.

🔹 Q2.

Assertion: A 1.5 kW heater used for 2 hours will consume 3 units of energy.
Reason: 1 unit of energy = 1 kilowatt-hour.

Answer: ✅ A
Explanation:
Energy consumed = 1.5 × 2 = 3 kWh = 3 units.
So, both assertion and reason are correct, and the reason explains the assertion.

🔹 Q3.

Assertion: The unit “watt” is used to measure electrical energy.
Reason: Energy = Power × Time.

Answer: ✅ D
Explanation:

• The assertion is false because watt is a unit of power, not energy.
• The reason is true as energy is calculated using power and time.

🔹 Q4.

Assertion: Joule is a smaller unit compared to kilowatt-hour for measuring electrical energy.
Reason: Kilowatt-hour is used for measuring energy consumed in industries and homes.

Answer: ✅ A
Explanation:
Both statements are true. Joules are very small compared to kWh, hence kWh is used commercially.

🔹 Q5.

Assertion: Energy consumed by a 100 W fan running for 10 hours is 10 kWh.
Reason: Energy = Power × Time

Answer: ✅ C
Explanation:

• Energy = 0.1 × 10 = 1 kWh, not 10 kWh.
• So, assertion is false, but reason is true.

🔹 Q6.

Assertion: Electric energy is expressed in kilowatt-hour because it is easier to handle large values.
Reason: 1 kilowatt-hour = 3.6×10³ joules.

Answer: ✅ C
Explanation:

• Assertion is true.
• Reason is false: 1 kWh = 3.6 × 10⁶ J, not 3.6×10³ joules.

📘 Worksheet: Commercial Unit of Electrical Energy (kWh)

Subject: Science (Physics) – Class 10
Topic: Commercial Unit of Electrical Energy
Time: 30 minutes  Max Marks: 20

✍️ Section A: Fill in the Blanks (1 mark each × 5 = 5 Marks)

1. The commercial unit of electrical energy is ___________.
2. 1 kilowatt-hour = ___________ joules.
3. 1 unit of electrical energy equals ___________ kilowatt-hour.
4. Electrical energy consumed = ___________ × time.
5. A 1.2 kW appliance running for 2.5 hours will consume ___________ kWh of energy.

✍️ Section B: Very Short Answer Questions (1 mark each × 3 = 3 Marks)

6. Why is kWh used as the commercial unit of energy instead of joules?
7. Convert 5 kWh to joules.
8. An electric bulb of 60 W is used for 5 hours daily. How much energy (in kWh) does it consume in 10 days?

🧮 Section C: Numerical Problems (2 marks each × 3 = 6 Marks)

9. Calculate the cost of using a 2 kW geyser for 3 hours per day for 10 days if the cost per unit is ₹6.50.
10. A household uses the following appliances:

• One 100 W fan for 10 hours/day
• Two 60 W bulbs for 5 hours/day
  Calculate the total energy consumed in 1 day in kWh.

11. An electric motor consumes 10 kWh of energy in 2 hours. What is the power rating of the motor in watts?

💡 Section D: Application-Based/Conceptual Questions (2 marks each × 3 = 6 Marks)

12. A company receives an electricity bill showing consumption of 600 units. If the rate per unit is ₹7.25, calculate the total bill amount.
13. A school uses a 1.5 kW water pump for 4 hours every day. How many units of energy does it consume in 20 days?
14. Why do electric companies prefer charging in kWh rather than joules? Give a suitable reason.

✅ Quick Revision

• 1 kWh = 3.6 × 10⁶ J
• Power (W) = Voltage (V) × Current (A)
• Energy (kWh) = Power (kW) × Time (h)
• Electricity Bill = Units consumed × Rate per unit

💡 Do You Know?

• 1 unit of electricity = 1 kilowatt-hour
• Domestic meters show readings in kWh (units)
• Power rating and time of usage directly affect your electricity bill!