100 PROBLEMS IN ELECTRICAL ENGINEERING PART – 07 – PROBLEMS ON RESISTANCE AND RESISTIVITY

PROBLEM – 01

Find the resistance of the aluminum conductor shown in figure. The length of conductor is 2 m and resistivity = 2.83 x 10^-5.

PROBLEM – 02

A liquid resistor consists of two metallic tubes radii R and r respectively. Each tube has length l. The space between tubes is filled sea water having resistivity of 0.2 ohm-metre. Find the resistance if R = 20 cm and r = 10 cm and l = 2m.

PROBLEM – 03

Find the resistance of aluminum tube of external diametre D, internal diametre d, length l and resistivity is 2.83 x 10^-8. If D = 20 cm, l = 6 cm and thickness of the tube is 1.5 cm. Find the resistance of the tube.

PROBLEM – 04

A liquid resistance has paralleled plate electrode. It is rated 50 kW, 220 V, d.c. supply. The liquid has resistivity of 0.5 ohm-metre. Find the distance between the plates if current density at electrode is 0.5 amps per square centimetre.

PROBLEM – 05

A resistor has cylindrical shape with radius r1 and length l1. It is recast with a triangular cross section (right angle triangle with sides r2) and appropriate length l2. Find its second resistance R2 in terms of first R1.

100 PROBLEMS IN ELECTRICAL ENGINEERING PART – 06 – FIVE PROBLEMS ON POWER PLANTS

FIVE PROBLEMS ON POWER PLANTS

PROBLEM – 01

Water for a hydro-electric is obtained from a reservoir with head of 150 m. Calculate the electrical generated per hour per cubic metre of water. If the hydraulic efficiency is 0.86 and electrical efficiency is 0.92.

PROBLEM – 02

A atomic power reactor can deliver 40 MW due to fission of each atom of Uranium-235. The energy released is 200 MeV. Calculate the mass of Uranium consumed per hour.

PROBLEM – 03

A 80 MW steam power plant uses coal of calorific value 6400 kcal per Kg. Thermal efficiency of the station is 30 percent and electrical efficiency is 92 percent. Calculate the coal consumption per hour, when the station is delivering its full rated output.

PROBLEM - 04

The thermal power station has an overall efficiency of 0.3 if 0.6 kg of coal is burnt to generated one kWh energy output, find the calorific value of coal.

PROBLEM – 05

A diesel station has the following data:

Fuel consumption per day = 1000 kg.

Units generated per day = 5000 kWh.

Calorific value of diesel = 10000 kcal per kg.

Alternator efficiency = 96 percent.

Engine mechanical efficiency = 95 percent.

Calculate (i) specific fuel consumption (ii) Overall efficiency (iii) thermal efficiency of engine.

100 PROBLEMS IN ELECTRICAL ENGINEERING PART – 05 – FIVE PROBLEMS ON HEATING EFFECT OF ELECTRIC CURRENT

FIVE PROBLEMS ON HEATING EFFECT OF ELECTRIC CURRENT

PROBLEM – 01

An electric oven has 3 heating elements of resistance 25 ohms each. They can be switched all in series or all in parallel. Calculate the rate of production of heat in calories per second in both cases when the supply voltage is 230 V.

PROBLEM – 02

An immersion water heater takes 30 minutes to heat 60 kg of water from 20 degree centigrade to boiling point. Calculate the power rating of the heater, assuming the heating equipment to have an efficiency of 90 percent.

PROBLEM – 03

A storage electric water heater is required to raise the temperature of 20 kg water from 20 degree centigrade to 80 degree centigrade in 45 minutes. Calculate the resistance of the heating element if the heater is to be used on a 230 V supply. Assume the efficiency of heater is 90 percent.

PROBLEM – 04

A soldering iron is rated at 25 watts when connected to a 75 watts when connected to a 230 V supply. If the soldering iron takes 5 minutes to heat a working temperature of 150 centigrade from 20 degree centigrade find the mass, assuming it to be made of copper. Specific heat capacity of copper is 390 J/k°C.

PROBLEM – 05

An electric kettle raises the temperature of 2 kg liters of water from 20 degree centigrade to 80 degree centigrade. If the efficiency of the heater is 85 percent. Calculate the energy consumed by the heater (a) in joules (b) in kWh. The specific heat capacity of the water 4190 J/KgK.

BASICS OF ELECTRICAL ENGINEERING - PART - 21 - INDEPENDENT AND DEPENDENT ENERGY SOURCES

INDEPENDENT ENERGY SOURCES

This type of sources, i.e., voltage or current is not changed by any variation in the connected network.

DEPENDENT ENERGY SOURCES

If the strength of voltage or current is changed due to any variation in the connected network, they are dependent source.

ALTERNATING SOURCES

Alternating source is sometimes used in which voltage or current varies with time, i.e., sinusoidally, exponentially and so on.

CONTROLLED SOURCES

Dependent sources are also known as controlled sources are of the following types.

1. VCVS – Voltage Controlled Voltage Source - Practically VCVS is an amplifier which amplifies V2 to µ times V2.

2. CCVS – Current Controlled Voltage Source – Practically CCVS is a resistance which converts current to voltage.

3. VCCS – Voltage Controlled Current Source – Practically VCCS is a conductance which converts voltage to current.

4. CCCS – Current Controlled Current Source – Practically CCCS is an amplifier which amplifies voltage to current.

SOURCE TRANSFORMATION

Any practical VOLTAGE SOURCE consists of an ideal voltage source in SERIES with its terminal resistance.

Any practical CURRENT SOURCE consists of an ideal current source in PARALLEL with its internal resistance.

The voltage and current sources are mutually transferable.

100 PROBLEMS IN ELECTRICAL ENGINEERING - PART – 04 – FIVE PROBLEMS ON MOTOR RATING

DIFFERENCE BETWEEN CRANE, LIFT AND HOIST

The major difference between crane and hoist is that crane can move an object in many directions including vertical and horizontal, hoist can lift object vertical only.

There is a significant difference between a ‘Lift’ and a ‘Hoist’ – a Lift is for public access and a Hoist is an industrial/commercial workhorse also suitable for many residential applications.

PROBLEM – 01

A crane motor lifts 4000 kg through a 20 m in 50 sec. Find the current and energy when supply voltage is 400 d.c and three phase 400 a.c. Assume motor efficiency is 60 percent and induction motor power factor is 0.8. 

PROBLEM – 02

An lift is required to raise a load of 10 tons through a height of 60 m. 25 percent of energy is lost in the motor and gearing. Calculate the energy is kWh supplied. If time required to raise the load is 54 minute. Find the kW rating of the motor and current taken by the motor. Supply voltage is 220 V d.c. Assume the efficiency of the motor is 80 percent.                           

PROBLEM – 03

An electric hoist makes 10 upward and 10 downward journeys per hour. During upward journey it raises a load of 10000 kg in 5 minutes to a height of 100 m. It returns empty during downward journey in 2 minutes. The weight of the cage is 1 ton and balance weight is 3000 kg. The efficiency of the hoist and motor is 0.8 and 0.88. Find (a) electrical energy input to the system in one upward and downward journey (b) energy consumed in one hour (c) horse power of the motor.

PROBLEM – 04

What must be the horse power of the engine to drive by means of a belt a generator for supplying 5000 lamps each lamp taking 0.5 A at 230 V. The line drop is 5 V and efficiency of the generator is 95 percent. There is a 2.5 percent lost in the belt drive.

PROBLEM – 05

A 220 V d.c. drives a pump lifting 1.5 m^3 of water per minute to a height of 15 m. If efficiency of the motor and pump is 60 percent determine (a) electrical input (b) the current taken from the supply. Assume 1 m^3 of water has a mass of 1000 kg.

100 PROBLEMS IN ELECTRICAL ENGINEERING PART – 03 – FIVE PROBLEMS ON COST OF ELECTRICAL ENERGY

PROBLEM – 01

An electric iron has a rating of 1.5 kW at 220 V and works for 10 hours a day, 26 days in a month. Calculate the current taken and for resistance of its heating element. Also, calculate the cost of electrical energy consumed in one month, if the cost of one kWh is Rs.2.25.

PROBLEM – 02

A 2 hp motor has an efficiency of 85 percent. What is (a) its electric power input in watts, (b) its energy consumption if it runs continuously for 10 hours, (c) the cost of energy consumption if the cost per unit is Rs.2.25 and (d) the current carrying capacity of its connecting wire, if it is operating from a 220 V supply.

PROBLEM – 03

A 250 ton train experiences wind resistance equivalent to 62.5 N/t. The operating efficiency of the driving motors 0.87 and the cost of electrical energy is Rs. 7.50 per unit. What is the cost of the energy required to make the train travel 1 km. If the train is supplied at a constant voltage of 2 kV and travels with a velocity of 80 km/h, what is the supply current?

PROBLEM – 04

An electric furnace is being used to melt 20 kg aluminium. The initial temperature of aluminum is 20 degree centigrade. Assume the melting point of aluminum to be 660 degree centigrade, its specific heat capacity to be 950 J/kg/ºC and its specific heat of latent heat of fusion to be 387000 J/kg. Calculate the power required to finish the conversion in 40 minutes, assuming the efficiency of conversion to be 80 percent. What is the cost of energy consumed if t cost of 1kWh is eighty rupee?

PROBLEM – 05

A diesel-electric generator set supplies an output of 50 kW. The calorific value of the fuel oil used is 10874.5 Kcal/kg. If the overall efficiency of the unit is 65 percent. Calculate (i) the mass of oil required per hour (ii) the electric energy generated per kg of diesel.