Junior Lineman / Energy Assistant — ITI Electrical Quick Book · Chapter 2

Basic Electricity

What to remember

Ohm's law: V = I × R. Power: P = V × I = I²R = V²/R. Energy: E = P × t; the commercial unit is the kWh (1 kWh = 1 unit = 3.6 million joules).
Kirchhoff's current law (KCL): the sum of currents entering a junction equals the sum leaving it. Voltage law (KVL): the algebraic sum of voltage drops and EMFs around any closed loop is zero.
Series resistors add; parallel conductances add. A lead-acid cell gives about 2 V, a Ni-Cd cell about 1.2 V, and a dry (Leclanche) cell about 1.5 V.

Electric charge, current, voltage and resistance

Matter is made of atoms. The electron carries a negative charge; the proton carries a positive charge. Electrons in the outer shell of a conductor are loosely held and are called free electrons.

Charge (Q) is measured in coulomb (C). One coulomb is about 6.24 × 10¹⁸ electrons.
Current (I) is the rate of flow of charge: I = Q / t. The unit is ampere (A). One ampere means one coulomb per second. Current is measured with an ammeter connected in series.
Potential difference (V) is the work done per unit charge: V = W / Q. The unit is volt (V). It is measured with a voltmeter connected in parallel.
EMF is the source voltage when no current is drawn. Terminal voltage is lower than EMF when the source delivers current, because of internal drop.
Resistance (R) opposes current. The unit is ohm (Ω). Conductance G = 1 / R, with the unit siemens (S) (older name: mho).

Conventional current flows from positive to negative. Electron flow is from negative to positive.

Resistance, resistivity and temperature

Resistance of a wire: R = ρ × l / A, where ρ is resistivity (ohm-metre), l is length and A is cross-section area.

Resistance is directly proportional to length.
Resistance is inversely proportional to area. Doubling the diameter makes the area four times, so the resistance falls to one-fourth.
If a wire is stretched to double its length (volume constant), its area halves, so resistance becomes four times.

Resistivity depends on the material and temperature, not on the size of the wire. Silver has the lowest resistivity among common metals, then copper, then aluminium. Copper and aluminium are the usual conductors for wires and cables. Nichrome and eureka (constantan) are high-resistance alloys used for heater elements and resistance boxes. Manganin is used in standard resistors because its resistance changes very little with temperature.

Temperature effect: For pure metals, resistance rises as temperature rises (positive temperature coefficient). For carbon, semiconductors and insulators, resistance falls as temperature rises (negative temperature coefficient). Formula: R₂ = R₁ [1 + α (t₂ − t₁)].

Material type	Examples	Effect of temperature rise on resistance
Pure metals	Copper, aluminium, silver	Increases
Carbon, semiconductors	Carbon, germanium, silicon	Decreases
Alloys (special)	Eureka, manganin	Almost constant

Resistor colour code: Black 0, Brown 1, Red 2, Orange 3, Yellow 4, Green 5, Blue 6, Violet 7, Grey 8, White 9. The first two bands give digits, the third band is the multiplier, and the fourth band is tolerance (gold 5%, silver 10%, no band 20%).

Ohm's law and resistor networks

Ohm's law holds at constant temperature: current through a conductor is directly proportional to the voltage across it. The graph of V against I is a straight line. Materials that obey it are called ohmic.

Series circuit: the same current flows in every resistor. Total R = R₁ + R₂ + R₃. Voltage divides in proportion to resistance.

Parallel circuit: the same voltage is across every branch. 1/R = 1/R₁ + 1/R₂ + 1/R₃. For two resistors, R = R₁R₂ / (R₁ + R₂). Current divides in inverse proportion to resistance. The total resistance is always less than the smallest branch.

Domestic loads are connected in parallel so each gets full supply voltage and one can be switched off without affecting the others. Fuses and switches are connected in series with the load.

Worked example 1: Resistors of 6 Ω and 3 Ω in parallel give (6 × 3) / (6 + 3) = 2 Ω. With a 12 V supply the total current is 12 / 2 = 6 A.

Worked example 2: Three 12 Ω resistors in parallel give 12 / 3 = 4 Ω.

Kirchhoff's laws

KCL (junction law): ΣI in = ΣI out. It is based on conservation of charge.
KVL (loop law): ΣE = ΣIR around a closed loop. It is based on conservation of energy.

Use of the laws: assume current directions, write a KCL equation at each junction and a KVL equation for each independent loop, then solve. A rise in potential is positive and a drop is negative while going round the loop.

Wheatstone bridge: a bridge of four resistors is balanced when P/Q = R/S. At balance, no current flows through the galvanometer. It is used for accurate measurement of an unknown resistance.

Work, power and energy

Power is the rate of doing work. Unit: watt (W). 1 W = 1 J/s. 1 kW = 1000 W. 1 horsepower (HP) = 746 W.
Energy = power × time. In SI the unit is joule (J) or watt-second. The commercial unit is kilowatt-hour (kWh), called a "unit" on the electricity bill.
Joule's law of heating: H = I²Rt joules. Heat produced is proportional to the square of current, to resistance and to time. One calorie equals 4.18 joules (approximately).
Efficiency η = output / input × 100%.

Worked example 3: A 2 kW heater runs for 5 hours. Energy = 2 × 5 = 10 kWh = 10 units.

Worked example 4: A 100 W lamp on 200 V draws I = 100 / 200 = 0.5 A. Its resistance = V²/P = 40000 / 100 = 400 Ω.

Worked example 5: A 5 HP motor with 80% efficiency draws input = 5 × 746 / 0.8 = 4662.5 W (about 4.66 kW).

Fuse wire is made of a low melting point alloy (tin-lead). It protects the circuit using the heating effect of current.

Cells and batteries

A cell converts chemical energy into electrical energy. A battery is a group of cells joined together.

Type	Examples	Remark
Primary cell	Leclanche (dry) cell, alkaline cell	Cannot be recharged; chemical action is not reversible
Secondary cell	Lead-acid, Ni-Cd, Li-ion	Can be recharged

Dry cell (Leclanche): zinc container is the negative electrode; carbon rod is the positive electrode; electrolyte is ammonium chloride paste; manganese dioxide is the depolariser. EMF about 1.5 V.

Lead-acid cell: positive plate is lead peroxide (PbO₂), negative plate is spongy lead (Pb), electrolyte is dilute sulphuric acid. Nominal EMF about 2 V per cell. A 12 V battery has 6 cells in series. On discharge, both plates turn to lead sulphate and the acid becomes weaker. On charge, the reverse happens. Specific gravity of electrolyte for a fully charged cell is about 1.2 to 1.28; it falls on discharge. It is measured with a hydrometer. Always add acid to water slowly, never water to acid. Distilled water is used for topping up. Sulphation (white deposit on plates) comes from leaving a battery discharged for long.

Nickel-cadmium (Ni-Cd) cell: alkaline electrolyte (potassium hydroxide), about 1.2 V per cell, long life, rugged.

Capacity is given in ampere-hour (Ah) = current × time. A 100 Ah battery can supply 5 A for about 20 hours.

Grouping of cells (n cells, each EMF E, internal resistance r):

Series: EMF = nE; internal resistance = nr. Gives higher voltage.
Parallel: EMF = E; internal resistance = r/n. Gives larger current capacity.

Terminal voltage V = E − Ir. Charging methods: constant current and constant voltage. Battery charging gives off hydrogen, so the room needs ventilation and no open flame.

Exam traps

Series resistors: add values. Parallel: add reciprocals. Do not mix them up.
Ammeter is connected in series; voltmeter in parallel.
In a pure metal resistance rises with temperature; in carbon and semiconductors it falls.
Doubling the diameter divides the resistance by four, not two.
1 kWh = 3.6 × 10⁶ J, not 3600 J. 1 HP = 746 W.
Power of a resistor on fixed voltage: P = V²/R, so a lower resistance gives more power. A 100 W lamp has lower resistance than a 40 W lamp of the same voltage rating.
Lead-acid cell is 2 V; Ni-Cd is 1.2 V; dry cell is 1.5 V.
EMF is measured with no load; terminal voltage is lower while the cell is delivering current.

One-liners

1. Unit of charge is the coulomb; unit of current is the ampere.
2. Resistivity unit is ohm-metre.
3. Conductance unit is siemens.
4. Ohm's law holds at constant temperature.
5. Total parallel resistance is less than the smallest branch.
6. KCL follows conservation of charge; KVL follows conservation of energy.
7. Wheatstone bridge balance condition: P/Q = R/S.
8. Joule's law: H = I²Rt.
9. A unit on the bill is 1 kWh.
10. Specific gravity of electrolyte is measured by a hydrometer.
11. Lead-acid cells in a 12 V battery: six, in series.
12. Gold fourth band on a resistor means 5% tolerance.

Practice questions

The SI unit of electric charge is
1. ohm
2. coulomb
3. volt
4. ampere
Answer
B. coulomb
Charge is measured in coulomb; ampere is the unit of current.
An ammeter is connected to a circuit
1. in series with the voltmeter only
2. in series with the load
3. across the supply only
4. in parallel with the load
Answer
B. in series with the load
An ammeter has very low resistance and must carry the load current, so it goes in series.
Two resistors of 6 Ω and 3 Ω are connected in parallel. The equivalent resistance is
1. 9 Ω
2. 4.5 Ω
3. 2 Ω
4. 18 Ω
Answer
C. 2 Ω
R = (6 × 3)/(6 + 3) = 18/9 = 2 Ω.
A 12 V supply is applied across a 4 Ω resistor. The current is
1. 48 A
2. 8 A
3. 3 A
4. 0.33 A
Answer
C. 3 A
I = V/R = 12/4 = 3 A.
Three resistors of 12 Ω each are connected in parallel. The total resistance is
1. 6 Ω
2. 12 Ω
3. 36 Ω
4. 4 Ω
Answer
D. 4 Ω
For equal resistors in parallel R = 12/3 = 4 Ω.
The resistance of a pure metallic conductor, with a rise in temperature,
1. remains constant
2. becomes zero
3. decreases
4. increases
Answer
D. increases
Pure metals have a positive temperature coefficient.
A 2 kW heater is used for 5 hours. The energy consumed is
1. 25 units
2. 10 units
3. 2.5 units
4. 7 units
Answer
B. 10 units
E = 2 kW × 5 h = 10 kWh = 10 units.
A 100 W lamp is connected to a 200 V supply. The current it draws is
1. 2 A
2. 20 A
3. 0.5 A
4. 0.2 A
Answer
C. 0.5 A
I = P/V = 100/200 = 0.5 A.
The resistance of a 100 W, 200 V lamp is
1. 2 Ω
2. 400 Ω
3. 200 Ω
4. 100 Ω
Answer
B. 400 Ω
R = V²/P = 40000/100 = 400 Ω.
A wire of resistance R is uniformly stretched to double its length (volume constant). Its new resistance is
1. R/2
2. 2R
3. R/4
4. 4R
Answer
D. 4R
Length doubles and area halves, so R = ρl/A becomes 2 × 2 = 4 times.
The diameter of a copper wire is doubled with length unchanged. Its resistance becomes
1. four times
2. one-half
3. one-fourth
4. double
Answer
C. one-fourth
Area is proportional to diameter squared, so area becomes four times and resistance one-fourth.
A current of 5 A flows through a 10 Ω resistor for 2 seconds. The heat produced is
1. 100 J
2. 250 J
3. 500 J
4. 50 J
Answer
C. 500 J
H = I²Rt = 25 × 10 × 2 = 500 J.
Resistors of 10 Ω, 20 Ω and 30 Ω are connected in series across 120 V. The current is
1. 0.5 A
2. 2 A
3. 12 A
4. 6 A
Answer
B. 2 A
Total R = 60 Ω; I = 120/60 = 2 A.
A battery of 100 Ah capacity supplies a steady 5 A. It can last for about
1. 500 hours
2. 5 hours
3. 95 hours
4. 20 hours
Answer
D. 20 hours
Time = Ah/I = 100/5 = 20 h.
A source of EMF 12 V and internal resistance 0.1 Ω delivers 10 A. Its terminal voltage is
1. 1 V
2. 13 V
3. 12 V
4. 11 V
Answer
D. 11 V
V = E − Ir = 12 − 10 × 0.1 = 11 V.
A 5 HP motor has an efficiency of 80%. The electrical input power is nearly
1. 4 kW
2. 4.66 kW
3. 6.2 kW
4. 3.73 kW
Answer
B. 4.66 kW
Output = 5 × 746 = 3730 W; input = 3730/0.8 = 4662 W.
A resistor has bands yellow, violet, red and gold. Its value and tolerance are
1. 47 Ω, 10%
2. 4700 Ω, 10%
3. 4700 Ω, 5%
4. 470 Ω, 5%
Answer
C. 4700 Ω, 5%
Yellow 4, violet 7, red = ×100, so 4700 Ω; gold means 5%.
In a balanced Wheatstone bridge P = 100 Ω, Q = 10 Ω and R = 50 Ω. The fourth arm S is
1. 0.2 Ω
2. 5 Ω
3. 500 Ω
4. 50 Ω
Answer
B. 5 Ω
P/Q = R/S gives S = RQ/P = 50 × 10/100 = 5 Ω.
A charge flow of 10 A for 5 seconds carries a charge of
1. 0.5 C
2. 15 C
3. 2 C
4. 50 C
Answer
D. 50 C
Q = I × t = 10 × 5 = 50 C.
Kirchhoff's current law is based on the conservation of
1. mass-energy of heat
2. momentum
3. charge
4. energy
Answer
C. charge
Charge cannot collect at a junction, so current in equals current out.
Kirchhoff's voltage law is based on the conservation of
1. charge
2. energy
3. power factor
4. resistance
Answer
B. energy
The net energy gained and lost around a closed loop is zero.
The commercial unit of electrical energy is
1. kilowatt-hour
2. watt
3. kilowatt
4. joule per second
Answer
A. kilowatt-hour
One kWh is one unit on the electricity bill.
The value of 1 kWh in joules is
1. 746 J
2. 1 × 10⁶ J
3. 3.6 × 10³ J
4. 3.6 × 10⁶ J
Answer
D. 3.6 × 10⁶ J
1000 W × 3600 s = 3,600,000 J.
In electrical work one horsepower is taken as
1. 550 W
2. 1000 W
3. 746 W
4. 100 W
Answer
C. 746 W
1 HP = 746 W in electrical work.
The nominal EMF of a fully working lead-acid cell is about
1. 1.5 V
2. 2 V
3. 1.2 V
4. 3.6 V
Answer
B. 2 V
Lead-acid is about 2 V per cell; Ni-Cd is 1.2 V and a dry cell is 1.5 V.
Which of the following is a primary cell?
1. Leclanche dry cell
2. Nickel-cadmium cell
3. Lithium-ion cell
4. Lead-acid cell
Answer
A. Leclanche dry cell
A dry cell cannot be recharged; the others are secondary cells.
The depolariser used in a Leclanche dry cell is
1. zinc chloride
2. potassium hydroxide
3. lead peroxide
4. manganese dioxide
Answer
D. manganese dioxide
Manganese dioxide removes hydrogen that would otherwise polarise the carbon rod.
The electrolyte of a lead-acid cell is
1. potassium hydroxide
2. distilled water only
3. ammonium chloride paste
4. dilute sulphuric acid
Answer
D. dilute sulphuric acid
Dilute H₂SO₄ is the electrolyte; KOH is used in Ni-Cd cells.
The state of charge of a lead-acid cell is checked using a
1. wattmeter
2. tachometer
3. hydrometer
4. megger
Answer
C. hydrometer
A hydrometer measures the specific gravity of the electrolyte.
Four identical cells each of 1.5 V are connected in series. The total EMF is
1. 3 V
2. 0.375 V
3. 6 V
4. 1.5 V
Answer
C. 6 V
Series cells add EMF: 4 × 1.5 = 6 V.
n identical cells of internal resistance r each are connected in parallel. The total internal resistance is
1. r/n
2. n²r
3. r
4. nr
Answer
A. r/n
Parallel internal resistances combine like parallel resistors: r/n.
Which alloy is preferred for standard resistors because its resistance hardly changes with temperature?
1. Copper
2. Manganin
3. Carbon
4. Tungsten
Answer
B. Manganin
Manganin and eureka have a very small temperature coefficient.
The unit of conductance is
1. ohm
2. siemens
3. henry
4. farad
Answer
B. siemens
Conductance G = 1/R is measured in siemens (mho).
Which of the statements is/are correct? 1. In a series circuit the same current flows through every resistor. 2. In a parallel circuit the same current flows through every branch.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
In a parallel circuit the voltage is common; the current divides among the branches.
Which of the statements is/are correct? 1. Fuses are connected in parallel with the load they protect. 2. Total resistance of resistors in parallel is less than the smallest branch resistance.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
A fuse is placed in series so that the load current passes through it.
Which of the statements is/are correct? 1. Resistance of carbon decreases when temperature rises. 2. Resistance of copper decreases when temperature rises.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Carbon has a negative coefficient; pure metals have a positive one.
Which of the statements is/are correct? 1. Heat produced is independent of the time for which the current flows. 2. Heat produced in a resistor is proportional to the square of the current.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
H = I²Rt, so heat grows with time as well.
Which of the statements is/are correct? 1. Terminal voltage of a cell is less than its EMF when current is drawn. 2. EMF of a cell is measured when a heavy current is drawn.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
EMF is the open-circuit voltage; internal drop lowers terminal voltage under load.
Which of the statements is/are correct? 1. A 40 W lamp consumes more energy than a 100 W lamp in the same time. 2. A 40 W lamp has more resistance than a 100 W lamp of the same voltage rating.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
R = V²/P is larger for lower power; energy is proportional to power for equal time.
Which of the statements is/are correct? 1. Specific gravity of the electrolyte of a lead-acid cell falls on discharge. 2. During discharge both plates of a lead-acid cell turn to lead sulphate.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
Acid is used up and both plates become PbSO₄ during discharge.
Which of the statements is/are correct? 1. When adding acid to water, the acid should be poured slowly into the water. 2. Ordinary tap water is best for topping up a lead-acid battery.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Distilled water is used for topping up; tap water carries impurities.
Which of the statements is/are correct? 1. A Wheatstone bridge cannot be used to measure resistance. 2. The Wheatstone bridge is balanced when no current flows through the galvanometer.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
The bridge is a standard method for accurate resistance measurement.
Which of the statements is/are correct? 1. Ni-Cd cells are secondary cells with about 1.2 V per cell. 2. A dry cell can be recharged many times like a Ni-Cd cell.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Dry cells are primary and are not meant to be recharged.
Which of the statements is/are correct? 1. Series connection of cells keeps the output voltage equal to that of one cell. 2. Parallel connection of cells increases the current capacity.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
Series connection adds voltages; parallel keeps voltage the same.
Which of the statements is/are correct? 1. Resistivity depends on the material of the conductor. 2. Resistivity depends on the length of the conductor.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Resistivity is a property of the material; resistance depends on length and area.

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1.The charge of two H + ions is ________.
2.The charge flowing through a circuit in 10 minutes is 300 C. Find the current drawn by the circuit.
3.The correct relation between charge(Q) following through a conductor, time(t) for which the charge follows and the current (I) following through the conductor is:
4.The formula of current I = _______ /time (t).
5.The generation of heat in a conductor due to electric current is known as:
6.The effective resistance of the parallel combination of two resistors is always _______
7.The electric dipole moment per unit volume is called ___________.
8.The electric current flowing through a metallic wire is directly proportional to the potential difference V across its ends, provided its _____ remains the same.
9.The electric ______ between two points in an electric circuit carrying some current is the work done to move a unit charge from one point to the other.
10.The electric power consumed by a resistor of resistance R, carrying current I, is _______

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