An Electric Circuit

• An electric circuit : A continuous and closed path of an electric current.

• Circuit Diagram: The diagram shows a simple circuit with a battery, a switch (plug
key), a bulb, an ammeter and a volt meter connected by wires. The conventional
current (I) flows from the positive terminal to the negative terminal of the battery.

• Components and Symbols:

o Ammeter (A): An instrument that measures electric current in a circuit..

o Switch (or plugkey): A conducting link between the cell and the bulb.

o Battery: A collection of cells.

o Bulb: An electrical load.

 o Wire: A conductor.

• Electric Charge:
o Charges are of two types: positive and negative.
o Positive charge: deficiency of electrons.
o Negative charge: excess of electrons.
o The SI unit of charge is the Coulomb (C).
o The charge on one electron is approx. 1.6 × 10-19 C.
o Like charges repel, and unlike charges attract.
o The total charge of an isolated system is always conserved.
o Charge exists in an integral multiple of the electronic charge (Q = ne).
NOTE : 1. EMF :The potential difference between the two terminals of a cell, when there is no
current flowing through the circuit. 2. Terminal voltage: The potential difference between the
two terminals of a cell, when there is current flowing through the circuit.

Electric Current
• Definition: The amount of charge flowing through a particular area in unit time.
OR: The rate of flow of charge through a cross-section of a conductor.
• Direction of Current:
o Conventional Current: The flow of positive charge was taken as the direction
of electric current.
o Electron Flow: In an electric circuit, the direction of electric current is opposite
to the direction of the flow of electrons (negative charges).
• Formula: I =Q/t Where:
o I = Electric current
o Q = Charge
o t = time
• SI Units:
o Current: Ampere (A)
o Charge: Coulomb (C)
o Time: seconds (s)
• Ampere: One ampere is the flow of one coulomb of charge per second.
o One coulomb is equivalent to the charge of approximately 6 × 1018 electrons.
• The charge of a single electron (e) is 1.6 × 10-19 C
• Note on Units: Small quantities of current are expressed in:
o milliampere (mA) = 10-3A
o microampere (μA) = 10-6A

Electric Potential and Potential Difference Electrons move only if there is a

difference of electric pressure, called the potential difference, along the conductor This
potential difference is produced by a battery or a cell. The chemical action within the battery
sets the charges in motion and produces an electric current.

• Definition of Potential Difference (V): Potential difference between two points is the
work done (W) to move a unit charge (Q) from one point to the other.
• Formula: Potential Difference (V) =Work done (W)/Charge (Q) V = W/Q
 • SI Units:
o Potential Difference: Volt (V)
o Work Done: Joule (J)
o Charge: Coulomb (C)
o Volt= joule/coulomb
• Definition of 1 Volt: 1 Volt is the potential difference between two points in a current-
carrying conductor when 1 Joule of work is done to move a charge of 1 Coulomb from
one point to the other.

Note on the Voltmeter

• Voltmeter: An instrument that measures potential difference (voltage).
• Connection: It is always connected in parallel across the two points where the
potential difference is to be measured.

Symbols of Commonly Used Components

Here are the components and their corresponding circuit symbols as listed in your notes:
Component Description Circuit Symbol
Electric Bulb / Lamp An electric light A circle with a cross inside:
source.

⊗Lamp

Switch (On) Allows current to flow

(closed circuit). A closed line:

Switch (Off) Stops the flow of

current (open circuit).
A broken line:

Plug Key (Closed) A type of switch that

is closed.

Plug Key (Open) A type of switch that

is open.

Wire A conductor that A straight line: ————

allows current to
flow.
 Component Description Circuit Symbol
A Wire Joint A point where two or A dot at the intersection.
more wires are
connected.

Wires Crossing Wires that cross One wire is shown "jumping" over the
paths but are not other.
connected.

Cell A single source of

electric potential.

Battery A combination of two

or more cells.

Resistor A component that A zigzag line: —\/\/\/\/\—

resists the flow of
current.

Variable Resistance A resistor whose A resistor symbol with an arrow through

(Rheostat) resistance can be it.
changed.

Ammeter An instrument that A circle with an 'A' inside:

measures electric
current.
 Component Description Circuit Symbol

Voltmeter An instrument that A circle with a 'V' inside:

measures potential
difference.

Types of Current:
Direct Current (DC): The current flows in only one direction and has a constant magnitude.
Alternating Current (AC): The current periodically reverses direction, and its magnitude
varies continuously (often sinusoidally).

Ohm's Law : ""If the physical condition of a conductor (length, temperature, mechanical
strain, etc.) remains unchanged ,the current flowing through a metallic wire is directly
proportional to the potential difference across its ends. It is not a universal law."(OR) "For an
ohmic resistor, and at constant temperature and pressure, the potential difference across it
is directly proportional to the current flowing through it."
A circuit diagram showing a battery, a switch, an ammeter, a voltmeter, a rheostat, and a
resistor labeled "Nichrome".
 A graph with the current (I) on the x-axis and the potential difference (V) on the y-axis,
illustrating the linear relationship.

Limitations:
1.Metals obey ohms law but semiconductors Si,Ge etc and that too at low temperatures
do not obey ohms law
2.Temperature should be constant due to resistance varies with temperature
Further notes :
• The mathematical representation: V α I or
• V/I = R or V = IR
• The definition of Resistance (R): "The property of a conductor to resist the flow of
charges."
• The SI unit of resistance: "ohm Ω" where ohm = volt / ampere.
• A definition of a Rheostat: "A device which is used to change the resistance in a circuit
i.e. regulates the current without changing voltage by increasing or decreasing the
length of the wire."(Variable resistance).

• Definition of Resistance (R): "Opposition to flow of electric current (motion of

electrons)."
• Electron Movement: It explains that electrons are not completely free to move in a
conductor due to the attraction of atoms, and their motion is "retarded by its
resistance."
• Conductors and Insulators:
o A component with low resistance is a "good conductor."
o A component with high resistance is a "bad conductor" or an "insulator."
o A component with "some appreciable resistance" is called a "resistor."
• Diagrams:
A simple circuit with a Nichrome wire and a bulb.

A circuit with a Nichrome wire of varying length and thickness to demonstrate the
effect on current (shown by an ammeter).

Conclusion: The text under the diagrams concludes:

o The current is "different for different components."
o "Ammeter reading decreases when the length of wire increased."
o "Ammeter reading increases when a thicker wire of same material" is used.

Laws of Resistance:
 o R α l (length of a conductor)
o R α 1/A (cross area of cross-section)
o R = ρ l/A, where ρ (rho) is "constant. It is electrical resistivity or the specific
resistance of the material of the conductor.
o The resistivity is numerically equal to the resistance of a substance having a unit
length and unit area of cross-section
• Units: The SI unit of ρ (rho) is Ωm (ohm-meter).
• Notes on Materials:
o Note ①: Metals and alloys (good conductors) have "very low resistivity" in the
range of 10-8 Ωm to 10-6 Ωm .Insulators (like rubber and glass) have resistivity of
1012 Ωm to 1017 Ωm
o Note ②: The resistivity of an alloy is "generally higher than that of its
constituent metals" and do not oxidise (burn) readily at higher temperatures. For
this reason electric heating devices like electric iron, toasters are made with
alloys like nichrome and manganese.
• Note 3: Tungsten is used as a filament in electric bulbs. Copper and Aluminium are
used for electrical transmission wires. The resistivities of Tungsten, Copper,
Aluminium and Silver at 20oC are 52.8 ohm m, 1.62 × 10-8 ohm m, 2.63 × 10-8 ohm m
and 1.60 × 10-8 ohm m
• Note 4 (Temperature vs. Resistivity):
1. Resistivity of a conductor increases linearly with increasing temperature.

2. Resistivity of a semiconductor (like an LED) decreases with an increase in

temperature.

3. Resistivity of insulators increases with a rise in temperature.

4. Certain alloys like nichrome and manganese have "vary negligible" temperature
resistivity, making them suitable for standard resistors.
Resistance of a system of Resistors:.
Resistors in Series:
• A circuit diagram shows three resistors (R1, R2, R3) connected end-to-end.
 o The current i through them will be the same.
o The sum of the potential differences (V1+V2+V3) across the resistors is equal to
the total potential difference (V)
o . V= V1+V2+V3
o By applying Ohms law V=iR,
iR =i R1+ iR2 + iR3
R = R1+ R2 +R3
• The equivalent resistance (RS) is given as: RS = R1+ R2 + R3

Resistors in Parallel:
• A circuit diagram shows three resistors (R1, R2, R3) connected with their ends joined
together.

The potential difference V across their ends is the same.

The sum of the currents (i1+i2+i3) through them is equal to the total current (i)
.i= i1+i2+i3
.By applying ohms law i=V/R
V/R=V/R1 + V/R2 + V/R3.
The equivalent resistance (Rp) is given as: 1/Rp = 1/R1 + 1/R2 + 1/R3. The total resistance in
a parallel circuit is always less than the smallest individual resistance: RP < min(R1/ R2/ R3).
Initial points:
o It is impractical to connect an electric bulb and an electric heater in series
because they require different values of current.
o When one component in a series circuit fails, the circuit is broken, and none of
the components work.
o The total resistance in a parallel circuit is decreased, which is useful when each
gadget has different resistance and current requirements.
• Heating effect of Electric current:
o The production of heat energy in a conductor by passing an electric current
through it is called the heating effect of the current.
• Derivation of Joule's law of heating:
o The work done (W) is to move a charge (Q) across a potential difference (V),
which is W = VQ.
o The power (P) supplied by the source is given as P = W/t = (VQ)/t = V(Q/t) = VI
(since I = Q/t).
o The energy supplied by the source in time t = Pt = (VI)t.
o This energy is dissipated in the resistor as heat, so the heat produced (H) is
equal to the energy supplied, leading to the formula H = VIt.
o By applying Ohm's law (V = IR) to the formula. This would lead to the more
common forms of Joule's law, H = I2Rt or H = V 2 × t/R. The heat (H)
produced in a resistor is directly proportional to I2, R, and t.

• Practical Applications of Heating Effect of Electric Current:

o List of Devices: Electric laundry iron, electric toaster, electric oven, electric
kettle, and electric heater are mentioned as devices based on Joule's heating.
o Producing Light: An electric bulb produces light using a tungsten filament with
a melting point of approximately 3380°C, kept in an unreactive nitrogen gas.
• Electric Fuse:
o A fuse is a safety device connected in series with the electric circuit.
o It's made of a metal or alloy (e.g., Al, Cu, Pb) with a very low melting point.
o If the current exceeds a specified safe value, the temperature of the fuse
increases, it melts, and breaks the circuit.
o An example is given for a 1 kW device operating at 220V, where the current is
calculated as I = P/V = 1000/220 = 4.54 A. A 5A fuse must be used in this case.
• Electric Power:
o Definition: The rate at which electrical energy is consumed or dissipated.
o Formula: Power (P) is defined as work done divided by time (W/t). It is also
given by the formula P = VI = I 2R = V 2/R =Qv/t
o Units: The unit of power is the Watt, which is equivalent to joules/second. A
practical unit is horsepower (hp), where 1 hp = 746 Watts.
o Electrical Energy: Electrical energy is defined as electrical power multiplied by
time.
o Commercial Unit: The commercial unit of energy is the kilowatt-hour (kWh). It
is defined as 1 kWh = 3.6 ×10 6J=3.6 MJ.
o Calculation: The notes show the conversion of 1 kWh to Joules:
▪ 1 Watt = 1 Volt * 1 Ampere = 1 VA
▪ 1 kWh = 1000 Watt * 3600 seconds
▪ 1 kWh = 3.6 ×10 6 Watt-seconds
▪ 1 kWh= 3.6 ×10 6 Joules (J).