Electricity — Quick Revision Pack

Chapter 11 | NCERT Class 10 Science | 10–15 min revision

2-Minute Recap

Electric current is rate of flow of charge: $I = Q / t$ . Potential difference drives current: $V = W / Q$ . Ohm’s law ( $V = I R$ at constant temperature) links $V$ , $I$ , and $R$ . Resistance depends on material, length, and area: $R = ρl / A$ . Resistors in series share the same current; in parallel they share the same voltage. Heating effect: $H = I^{2} R t$ . Power: $P = V I = I^{2} R = V^{2} / R$ . Commercial unit of energy: $1 kWh = 3.6 \times 1 0^{6} J$ .

Memory Tricks (Mnemonics)

Trick	Meaning
$V = I R$ → “Very Important Relation”	Ohm’s law core.
Ammeter = “Add in series”	Ammeter always in series.
Voltmeter = “V across = parallel”	Voltmeter always in parallel.
Series: “Same I, Resistances add”	$R_{s} = R_{1} + R_{2} + \dots$
Parallel: “Same V, Reciprocals add”	$\frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots$
“Parallel is Petite”	$R_{p}$ is less than the smallest branch resistance.
$R = ρl / A$ → “Long thin wire resists more”	Stretch a wire ⇒ $l$ up, $A$ down ⇒ $R$ up a lot.
Joule: “ $I^{2} R t$ heats”	Heating devices use high $I$ and suitable $R$ .
$P = V I$ → “Power Very Intense”	Also $I^{2} R$ and $V^{2} / R$ .
$1$ kWh = $3.6 \times 1 0^{6}$ J	Board conversion classic.

One-Liner Definitions (Board Gold)

Term	One-liner
Electric current ( $I$ )	Rate of flow of electric charge through a conductor: $I = Q / t$
Ampere	SI unit of current — $1$ A = $1$ C flowing per second
Potential difference ( $V$ )	Work done to move unit charge between two points: $V = W / Q$
Volt	SI unit of PD — $1$ V = $1$ J/C
Resistance ( $R$ )	Opposition offered by a conductor to current: $R = V / I$
Ohm’s law	At constant temperature, $V \propto I$ for a metallic conductor
Resistivity ( $ρ$ )	Resistance of a wire of unit length and unit cross-sectional area
Series combination	End-to-end connection; same current through each resistor
Parallel combination	Side-by-side connection across same two points; same PD across each
Joule’s heating	Heat produced in a resistor: $H = I^{2} R t$
Electric power ( $P$ )	Rate of consumption of electrical energy
Kilowatt-hour (kWh)	Commercial unit of electrical energy
Fuse	Safety device of low melting-point wire that melts on excess current
Conventional current	Direction of flow of positive charge (opposite to electron flow)

Must-Write Equations / Formulae

Formula	Units	When to use
$I = \frac{Q}{t}$	A, C, s	Charge / time numericals
$V = \frac{W}{Q}$	V, J, C	Work and PD
$V = I R$	V, A, $Ω$	Ohm’s-law problems
$R = ρ \frac{l}{A}$	$ρ$ in $Ω m$	Length, thickness, material
$R_{s} = R_{1} + R_{2} + R_{3}$	$Ω$	Series equivalent
$\frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \frac{1}{R _{3}}$	$Ω$	Parallel equivalent
Two resistors parallel: $R_{p} = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$	$Ω$	Quick two-branch case
$H = I^{2} R t = V I t = \frac{V ^{2}}{R} t$	J (or cal if asked)	Heating effect
$P = V I = I^{2} R = \frac{V ^{2}}{R}$	W	Power / ratings
Energy $E = P \times t$	J or kWh	Bills / consumption
$1 kWh = 3.6 \times 1 0^{6} J$	—	Unit conversion

Circuit instrument rule: ammeter series (ideal $R \approx 0$ ); voltmeter parallel (ideal $R$ very large).

Flowchart / Decision Map

(in words)

One resistor, find $V$ , $I$ , or $R$ ? → Ohm’s law $V = I R$ .
Wire stretched / cut / diameter changed? → $R = ρl / A$ (often volume constant ⇒ $A \propto 1/ l$ ).
Several resistors?
- Identify which share the same current (series) vs same PD (parallel).
- Reduce step by step to $R_{eq}$ .
- Then $I_{total} = V / R_{eq}$ ; split currents in parallel branches if needed.
Heat / filament / heater? → $H = I^{2} R t$ (or equivalent forms).
Appliance rating / electricity bill? → $P = V I$ ; energy $= P t$ ; convert to kWh for cost.
Household wiring reason? → Parallel: same voltage, independent switches, if one fails others work.

Board Keywords to Underline

electric current, potential difference, Ohm’s law, resistance, resistivity, series, parallel, equivalent resistance, Joule’s law of heating, electric power, kilowatt-hour, fuse, overloading, conventional current, ammeter, voltmeter

Common Mistakes (Don't Lose Marks)

Putting ammeter in parallel or voltmeter in series.
Adding resistances in parallel as $R_{1} + R_{2}$ (must use reciprocals).
Forgetting that $R_{p} <$ smallest $R$ — sanity-check failed.
Using $P = I^{2} R$ when only $V$ and $R$ are easy — pick the matching form.
Leaving energy in joules when the question asks kWh (or vice versa).
Wrong SI unit of resistivity (it is $Ω m$ , not $Ω$ /m).
Assuming series resistors have the same voltage (they have the same current, voltages add).
Ignoring “constant temperature” when stating Ohm’s law.
Power of heater written as $P = I R$ (missing square / wrong formula).
Sign / direction confusion: conventional current opposite to electron flow — mention if asked.

5 Rapid Fire (+ answers)

Q: SI unit of resistivity?
A: $Ω m$ .
Q: Equivalent resistance of $2 Ω$ , $3 Ω$ , $6 Ω$ in parallel?
A: $1 Ω$ (since $\frac{1}{R _{p}} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1$ ).
Q: Why are domestic appliances connected in parallel?
A: Each gets the same supply voltage; can be operated independently; equivalent resistance stays low enough for required current.
Q: Heat produced in a $4 Ω$ resistor carrying $2$ A for $10$ s?
A: $H = I^{2} R t = 4 \times 4 \times 10 = 160 J$ .
Q: $1$ kWh equals how many joules?
A: $3.6 \times 1 0^{6} J$ .

Night-Before Checklist

Definitions: current, PD, resistance, resistivity, power, kWh
Ohm’s law statement + $V = I R$ graph idea (straight line through origin)
$R = ρl / A$ and effect of stretching a wire
Series vs parallel table (same $I$ / same $V$ ; $R_{s}$ ; $R_{p}$ )
One mixed circuit reduction practised
$H = I^{2} R t$ and all three power formulae
$1 kWh = 3.6 \times 1 0^{6} J$ + one bill-style numerical
Fuse / overloading one-liners )