Understanding Electric Power: Analytical Questions

 Step-by-Step Solutions to Class 10 Electricity Problems

Recall Concepts:

Potential Difference or Voltage is mathematically written as follows:

Voltage (V) = Work done (W) / Charge(Q)

Or W = V x Q ------------- (i)

Energy: Energy is the ability to do work.

From equation (i), we get -

Electrical Energy (E) = V × Q --- (ii)

Power: Power is the rate at which work is done or the rate at which energy is transferred or converted.

Power = Work done or Energy transferred / Time

P = E / t ------------- (iii)

Using (ii) in (iii), we have

P = V x Q / t

P = V x I ———- (iv

{from definition of Current (I) = Q / t}

The SI unit of electric power is watt (W). It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V. Thus,

1 W = 1 volt × 1 ampere = 1 V A

The unit watt is small; therefore, Kilowatt is used.)

Electrical Power = Voltage x Current,

the unit is watts (W)

We know

Energy = Power x Time

where unit of Energy is Joule, unit of Power is Watt

Ex. If I purchase a bulb of 60 Watt, it means it consumes 60 Joules of Electrical Energy per second.

Energy supplied to the circuit by the source in time t,

E = P x t

= V x I x t {from (iv)}

The unit for electric energy is watt hour (W h).

The commercial unit of Electric energy is kilowatt hour (kW h),

1 kW h = 1000 watt × 3600 second

1 KW h = 3.6 x 10⁶ Watt-Second

1 KW h = 3.6 x 10⁶  Joule (J)

 

1. In a house, 3 bulbs of 100 watt each lighted for 5 hours daily, 2 fans of 50 watt each used for 10 hours daily and an electric heater of 1.00 kW is used for half an hour daily. Calculate the total energy consumed in a month of 31 days and its cost at the rate of Rs. 3.60 per kWh.

Solution:

To calculate the total energy consumed and its cost:

Step 1: Calculate Daily Energy Consumption

1. Bulbs:

Power = 3 × 100 W = 300 W

Energy = 300 W × 5 hours 

             = 1500 Watt- hour

             = 1.5 kWh/day or 1.5 Units /day

2. Fans:

Power = 2 × 50 W 

           =100 W

Energy = 100 W × 10 hours 

             = 1000 Wh 

             = 1 kWh/day or 1 Unit/day

3. Heater:

Power =1 kW 

           =1000 W

Energy =1000 W × 0.5 hours 

             = 500 Wh

             = 0.5 kWh/day or 0.5 Units/day

Step 2: Total Daily Energy Consumption

Total Daily Energy = 1.5 kWh + 1 kWh + 0.5 kWh 

                               = 3 kWh/day or 3 Units/day

Step 3: Total Energy Consumption in 31 Days

Total Energy for 31 Days = 3 kWh/day × 31 days 

                                          = 93 kWh

Step 4: Calculate the Cost

Cost = 93 kWh × 3.60 Rs/kWh 

        = 334.80 Rs

Total energy consumed in 31 days is 93 kWh or 93 Units, and the Bill amount is Rs. 334.80.

2. An electric motor takes 5 A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h.

Solution:

Given:

   Voltage          = 220 Volt

 Current drawn = 5 A

               Time = 2 hours

                        = 2 x 60 x 60 Seconds

                        = 7200 Seconds

To find Power of the Motor

Recall,

Power (P) = Voltage (V) x Current (I)

P = 220 x 5 

   = 1100 Watt

Now, to find Energy Consumed

Energy = Power x Time

             = 1100 x 7200

             = 7920000 Joules

             = 7.92 x 10⁶ Joules

3. Compute the heat generated while transferring 96000 coulombs of charge in two hours through a potential difference of 40 V.

Solution:

Recall Joule’s Law of Heating, Heat generated is given by-

 H = I² x R x t   or H = V x I x t           {⸪ From ohm’s law V = I x R}

Given:

 Charge (Q) = 96000 Coulombs

 Voltage (V) = 40 Volts, 

           Time = 2 hours 

                    = 2 x 60 x 60 

                    = 7200 seconds

To find current (I),

We know I = Q/t

                  = 96000/7200

                  = 13.33 A

Now, H = 40 x 13.33 x 7200 Joules

           = 3,839,520 Joules or 3.84×10⁶ Joules