Electricity — Class 10 Science

When a potential difference is applied across a conductor, electric charges (electrons) begin to flow through it. This flow of electric charge is called electric current.

Formula: I = Q / t
where I = current (Ampere), Q = charge (Coulomb), t = time (second)

Key Points:

• SI unit of current: Ampere (A)
• SI unit of charge: Coulomb (C)
• 1 Ampere = 1 Coulomb per second (1 A = 1 C/s)
• Charge of 1 electron = 1.6 × 10⁻¹⁹ C
• Conventional current flows from positive (+) to negative (−) terminal
• Electron flow is from negative (−) to positive (+) terminal (opposite direction!)
• Current is measured using an ammeter connected in series

Just as water flows from a higher level to a lower level, electric current flows from a point of higher potential to a point of lower potential.

Potential Difference: V = W / Q
where V = potential difference (Volt), W = work done (Joule), Q = charge (Coulomb)

Key Points:

• Electric potential: Work done in bringing a unit positive charge from infinity to a point
• Potential difference between two points = work done to move a unit charge from one point to another
• SI unit: Volt (V). 1 Volt = 1 Joule / 1 Coulomb
• Potential difference is measured using a voltmeter connected in parallel
• The battery (or cell) maintains the potential difference across a circuit

A circuit diagram is a simplified representation of an electric circuit using standard symbols. It is essential to know these symbols for board exams.

Important Rules for Circuit Diagrams:

• Always use standard symbols (never draw actual pictures of components)
• Draw circuits with straight lines meeting at right angles
• Ammeter (A) is connected in series — current flows through it
• Voltmeter (V) is connected in parallel — measures potential difference across a component
• The longer line in a cell symbol represents the positive terminal

Ohm’s Law states that the potential difference (V) across a conductor is directly proportional to the current (I) flowing through it, provided the temperature remains constant.

V = I × R
V = Potential difference (Volt), I = Current (Ampere), R = Resistance (Ohm, Ω)

Key Points:

• The V-I graph is a straight line passing through the origin
• The slope of V-I graph gives resistance (R): R = V/I
• Ohm’s law is valid only at constant temperature
• Conductors that obey Ohm’s law are called ohmic conductors (e.g., metals)
• Conductors that don’t obey Ohm’s law are called non-ohmic conductors (e.g., diode, LED)

Other forms of the formula:

• V = IR (to find voltage)
• I = V/R (to find current)
• R = V/I (to find resistance)

Resistance is the property of a conductor that opposes the flow of electric current through it. It is like friction for electricity.

R = V / I (from Ohm’s law)
SI unit of resistance: Ohm (Ω)

Factors Affecting Resistance:

1. Length (l): R ∝ l — Longer wire = more resistance
2. Area of cross-section (A): R ∝ 1/A — Thicker wire = less resistance
3. Material: Different materials have different resistivities
4. Temperature: For metals, resistance increases with temperature

Resistivity Formula: R = ρl / A
where ρ (rho) = resistivity of the material, l = length, A = area of cross-section
SI unit of resistivity: Ωm (ohm-metre)

Important about Resistivity:

• Resistivity depends only on the material and temperature, not on length or area
• Metals have very low resistivity (good conductors): Silver, Copper, Aluminium
• Insulators have very high resistivity: Rubber, Glass, Wood
• Alloys (like nichrome, constantan) have higher resistivity than pure metals and are used in heating elements

When resistors are connected end-to-end, they are said to be in series. The same current flows through each resistor.

Total Resistance in Series:
Rₛ = R₁ + R₂ + R₃

Total Voltage: V = V₁ + V₂ + V₃
Current: I (same through all)

Properties of Series Combination:

• Current is same through all resistors
• Voltage is divided among resistors (V = V₁ + V₂ + V₃)
• Total resistance is the sum of individual resistances
• Total resistance is always greater than the largest individual resistance
• If one resistor breaks, the entire circuit breaks (current stops flowing)

Derivation:

By Ohm’s law: V₁ = IR₁, V₂ = IR₂, V₃ = IR₃

Total voltage: V = V₁ + V₂ + V₃ = IR₁ + IR₂ + IR₃ = I(R₁ + R₂ + R₃)

Since V = IRₛ, therefore Rₛ = R₁ + R₂ + R₃

When resistors are connected between the same two points, they are said to be in parallel. The same voltage acts across each resistor.

Total Resistance in Parallel:
1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃

Total Current: I = I₁ + I₂ + I₃
Voltage: V (same across all)

Properties of Parallel Combination:

• Voltage is same across all resistors
• Current is divided among resistors (I = I₁ + I₂ + I₃)
• Total resistance is always less than the smallest individual resistance
• If one resistor breaks, others keep working (current has alternate paths)

Derivation:

By Ohm’s law: I₁ = V/R₁, I₂ = V/R₂, I₃ = V/R₃

Total current: I = I₁ + I₂ + I₃ = V/R₁ + V/R₂ + V/R₃ = V(1/R₁ + 1/R₂ + 1/R₃)

Since I = V/Rₚ, therefore 1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃

Understanding the differences between series and parallel circuits is crucial for board exams. Here is a complete comparison:

Why is household wiring done in parallel?

• Each appliance gets the same voltage (220 V)
• Each appliance can be switched on/off independently
• If one appliance fails, others continue to work
• Total resistance is reduced, so different appliances can draw different currents as needed

Numerical Example:

Three resistors of 2Ω, 3Ω, and 6Ω:

• In series: Rₛ = 2 + 3 + 6 = 11 Ω
• In parallel: 1/Rₚ = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1, so Rₚ = 1 Ω

When electric current flows through a conductor, it gets heated. This is called the heating effect of electric current or Joule heating.

Joule’s Law of Heating:
H = I²Rt
where H = heat produced (Joule), I = current (A), R = resistance (Ω), t = time (s)

Also: H = VIt = V²t/R

Key Points:

• Heat produced is proportional to square of current (H ∝ I²)
• Heat produced is proportional to resistance (H ∝ R)
• Heat produced is proportional to time (H ∝ t)
• This is why alloys like nichrome are used in heating elements (high resistance, high melting point)

Applications of Heating Effect:

• Electric heater / iron / toaster: Nichrome wire gets hot when current passes
• Electric bulb: Tungsten filament glows white-hot (melting point ~3380°C)
• Electric fuse: Thin wire of low melting point metal that melts and breaks the circuit when excessive current flows (safety device)

Why tungsten for bulb filaments?

• Very high melting point (3380°C)
• Does not burn easily at high temperatures
• Bulbs are filled with inert gas (nitrogen, argon) to prevent oxidation

Electric power is the rate at which electrical energy is consumed or dissipated in a circuit.

Electric Power: P = V × I

Also: P = I²R = V²/R

SI unit: Watt (W). 1 W = 1 V × 1 A

Other Units of Power:

• 1 kilowatt (kW) = 1000 W
• 1 horsepower (HP) = 746 W

Electrical Energy: E = P × t

Commercial unit of energy: kilowatt-hour (kWh) or 1 unit
1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J

Key Points:

• Watt (W) is the SI unit of power
• The commercial unit of electrical energy is kWh (unit)
• 1 kWh = 3.6 × 10⁶ Joules
• Electricity bill is calculated in units (kWh)
• A 100 W bulb used for 10 hours = 100 × 10 = 1000 Wh = 1 kWh = 1 unit

Electricity Bill Calculation:

Energy consumed (kWh) = (Power in watts × Time in hours) / 1000

Example: A 2 kW heater used for 3 hours daily for 30 days:

• Energy = 2 × 3 × 30 = 180 kWh = 180 units
• If rate = ₹5 per unit, bill = 180 × 5 = ₹900