Electricity is the flow of electric charge — specifically electrons — through a conductor. Think of it like water flowing through a pipe. The pipe is the wire, water pressure is voltage (V), the rate of flow is current (I), and anything that restricts flow is resistance (R).
Here is the analogy that sticks: imagine a narrow pipe connecting two tanks at different heights. The height difference drives water from high to low — that is voltage doing the same job in a circuit, pushing current from high potential to low. A thicker pipe allows more flow with less resistance. Squeeze the pipe (increase resistance) and the flow drops.
Three core quantities you must own:
Ohm's Law ties them together: V = IR. This one equation generates most of the numerical questions you will see.
Power is how fast electrical energy is used: P = VI = I²R = V²/R. In exam questions, you will almost always get two out of three variables and need to find the third. The formula P = I²R is the most commonly tested form.
Electrical energy consumed = P × t (Power × time). When you see "units consumed" or "kWh", you are working with this. 1 unit = 1 kWh = 1000 W used for 1 hour.
The difference between series and parallel circuits shapes everything about how household wiring and exam questions work. Series means resistors are chained end-to-end; parallel means they share the same two terminals. Your home runs on parallel — so each appliance gets full voltage and switching one off does not kill the others.
V = IR holds when temperature is constant. For a given material, resistance depends on:
R ∝ LR ∝ 1/AR = ρL/ALow resistivity = good conductor. Metals like copper and silver have very low resistivity — that is why wires are made of copper. Nichrome (an alloy of nickel and chromium) has high resistivity, which is why it is used in heaters. Among pure metals, chromium has lower resistivity than nichrome, iron, or nickel — important for the PYQ you will see below.
Resistors R₁, R₂, R₃ in series:
R_total = R₁ + R₂ + R₃ (resistances add up — always higher than any individual)V₁/V₂ = R₁/R₂The key rule: in series, more resistance = more voltage drop across that component.
So for 50 Ω and 100 Ω in series with the same current I flowing through both:
V₅₀ = I × 50V₁₀₀ = I × 100 = 2 × (I × 50)The 100 Ω resistor gets exactly double the voltage of the 50 Ω one.
Resistors in parallel:
1/R_total = 1/R₁ + 1/R₂ + ... (always lower than the smallest individual resistance)Household wiring is parallel because:
Three equivalent forms — use whichever two quantities are given:
| Given | Formula |
|---|---|
| V and I | P = VI |
| I and R | P = I²R |
| V and R | P = V²/R |
Energy calculation:
Energy (kWh) = Power (kW) × Time (hours)
Convert watts to kilowatts by dividing by 1000. Then multiply by hours. The result is directly in units (kWh).
AC is used for long-distance transmission because its voltage can be stepped up or down using transformers — DC cannot be transformed this way.
When a conductor moves through a magnetic field (or when a magnetic field changes around a conductor), an EMF (electromotive force) is induced — this is Faraday's Law. This is the principle behind:
For generators, use Fleming's Right-Hand Rule: stretch thumb, index, and middle finger of the right hand mutually perpendicular. Thumb = motion direction, Index = magnetic field, Middle = induced current direction.
A current-carrying wire creates a magnetic field around it — this is the basis of electromagnets. The strength of the magnetic field increases with:
Draw a triangle with V at top, I at bottom-left, R at bottom-right. Cover what you want to find:
For power, draw a second triangle: P at top, I at bottom-left, V at bottom-right.
Then combine: since V = IR, substitute into P = IV to get P = I²R or P = V²/R.
Standard approach (memorising 6 separate formulas): 3-4 minutes to recall under pressure. With both triangles drawn at the top of your rough sheet before the exam starts: 15 seconds to answer any power/voltage/current/resistance question.
Series: Same Current, resistances Add → remember "SCA" (Series: Current same, Add resistances). Parallel: Same Voltage, Reciprocals add → remember "SVR" (Same Voltage, Reciprocals).
For a two-resistor parallel shortcut: R_total = (R₁ × R₂) / (R₁ + R₂) — product over sum. No need to compute reciprocals.
Standard method (computing 1/R₁ + 1/R₂ with LCM): 5 steps. Product-over-sum shortcut: 2 steps. Saves roughly 30 seconds on a numerical question.
The trap: question gives power in Watts, but energy must be in kWh (units).
Lock this sequence: W ÷ 1000 = kW → kW × hours = units.
For the 100 W bulb question: 100 ÷ 1000 = 0.1 kW. Time = 10 h/day × 3 days = 30 hours. Energy = 0.1 × 30 = 3 units. Done in under 20 seconds once you have the conversion locked.
Most wrong answers come from forgetting to divide by 1000. Do the division first, always.
Best conductors in order (lowest to highest resistivity): Silver → Copper → Gold → Aluminium → Iron → Nichrome.
Key anchors: Copper is the standard wire material. Nichrome is the heater wire. For exam options that mix pure metals with alloys, the pure metal almost always wins. Nichrome is an alloy — it will lose to chromium (a pure metal component) in conductivity comparisons.
Recalling this costs 3 seconds vs. trying to reconstruct from scratch under exam pressure.
In a series circuit, voltage across each resistor is directly proportional to its resistance. No current calculation needed.
V₁ : V₂ = R₁ : R₂
For 50 Ω and 100 Ω in series across a total voltage: V distributes as 50:100 = 1:2. So the 100 Ω gets twice the voltage of the 50 Ω. Write the ratio, read the answer — 4 steps instead of 8. Saves about 40 seconds.
When you see an electricity question in the exam hall, run this decision tree in your head:
Is it a conceptual question (conductor, AC/DC, circuit type)?
Is it a numerical question?
Is it a circuit configuration question?
Never start a numerical without writing down what is given and what is asked. One wrong substitution wastes more time than the 10 seconds of setup saves.
Why this question: Tests knowledge of material properties — resistivity is a standard topic, and the trap here is confusing Nichrome (a common alloy) with its constituent metals.
Solving path: Eliminate on knowledge of material types. Nichrome is a nickel-chromium alloy — it has high resistivity by design (used in heaters). Chromium as a pure metal has significantly lower resistivity than the alloy Nichrome. Between iron, nickel, and chromium as pure metals, chromium has the lowest resistivity among these options. Answer: Chromium.
Why this question: Classic P = I²R application. The two-step structure (find P first, then R) is the standard format Bihar Police uses for heater/appliance numericals.
Solving path: Step 1 — Power = Work/Time = 200/2 = 100 W. Step 2 — Use P = I²R: 100 = (2)² × R = 4R. Therefore R = 100/4 = 25 Ω. The trap options (10 Ω, 20 Ω, 5 Ω) catch you if you forget to square the current or use the wrong formula.
Why this question: A direct conceptual question about household wiring — one of the most frequently tested facts in this chapter across multiple state police exams.
Solving path: The reason is functional: parallel connection ensures each appliance gets the same 220 V regardless of what else is running, and allows independent switching. Series would mean all appliances share one current path — switching one off kills all. Answer: in parallel.
Why this question: Energy unit conversion is the single most common arithmetic trap in electricity questions. This tests whether you correctly convert W to kW before multiplying by hours.
Solving path: Power = 100 W = 0.1 kW. Total time = 10 hours/day × 3 days = 30 hours. Energy = 0.1 kW × 30 h = 3.0 kWh = 3 units. The traps at 1.08 and 2.16 catch you if you calculate for only 1 or 2 days, or forget the kW conversion.
Why this question: This is a multi-statement series circuit question in Hindi — tests voltage division logic and whether you can eliminate false statements quickly.
Solving path: In series, current is the same through both resistors. Voltage across each = I × R, so V₅₀ = 50I and V₁₀₀ = 100I. Statement (i): voltages are different — TRUE. Statement (ii): voltages are equal — FALSE. Statement (iii): V₅₀ is double V₁₀₀ — FALSE (it is half, not double). Statement (iv): V₁₀₀ is double V₅₀ — TRUE. Correct pair: (i) and (iv).
Forgetting to convert W to kW before computing units consumed. Multiplying 100 W × 30 hours gives 3000, which you then wrongly read as 3000 kWh instead of 3 kWh. Always divide watts by 1000 first.
Using V = IR to find R when you actually have P and I. The correct path is P = I²R, rearranged to R = P/I². Plugging into V = IR without finding V first is an extra step that introduces errors.
Assuming nichrome is a better conductor because it is named alongside chromium. Nichrome is a high-resistivity alloy. Its component metals (nickel, chromium) are better conductors than the alloy itself.
Getting series voltage division backwards. In series, the larger resistor gets the larger voltage share — not the smaller. Many students instinctively invert this, thinking smaller resistance = more voltage.
Thinking parallel circuits always have lower total current. Adding more appliances in parallel increases total current drawn from the source, even though each appliance still sees the same voltage. The total resistance drops, so total current rises (I = V/R_total).
Confusing Fleming's Left-Hand Rule (motor) with Right-Hand Rule (generator). Left = current in, force out (motor). Right = motion in, current out (generator). The word "motor" has more letters than "generator" — no, that is not helpful. Better anchor: Left = eLectric motor.