An electric circuit is simply a closed path that lets charge flow from one terminal of a cell back to the other. For CDS Science, circuits are gold: master a handful of rules — Ohm's law, series and parallel resistance, and P = VI — and you can crack the bulk of the electricity questions, which appear in almost every paper as quick one-step numericals or sharp concept checks.
Why this topic matters in CDS
Electricity is among the most predictable scoring areas of the CDS Science section. Year after year the paper asks about series and parallel connections, the heating effect, bulb and appliance ratings, and the cost of electrical energy. These are not memory-heavy — they rest on three or four formulas you can master in an afternoon.
The questions come in two flavours. The first is conceptual: why are house appliances wired in parallel, why does a thick wire have lower resistance, why does a bulb glow brighter on higher voltage. The second is a single-step numerical: find the current, the equivalent resistance, the power, or the monthly bill. Both reward clear fundamentals over heavy calculation.
NCERT builds this gradually — electric current and circuits in Class 10, then a fuller treatment of current electricity in Class 12. The CDS paper draws from this entire range, so a firm grip here also strengthens the closely linked topics of resistors, fuses and the heating effect. Because the same ideas reappear across General Knowledge and even General Science questions in other defence exams such as AFCAT and NDA, the time you invest here pays back many times over.
The trick to scoring fast is to recognise the underlying pattern quickly. A long word problem about an iron, a geyser and a bulb is, at heart, just a power-and-energy sum. A diagram of three resistors is just a series-and-parallel reduction. Train your eye to strip away the story and spot the formula, and these questions become some of the easiest marks on the whole paper.
Almost every electricity numerical reduces to Ohm's law (V = IR) plus a power formula. Memorise the power triangle — P = VI = I²R = V²/R — and you can attack any version the examiner throws at you.
What a circuit is: current, voltage, resistance
A circuit needs a source (cell or battery), conductors (wires), a load (bulb, resistor, appliance) and usually a switch. When the switch is closed the path is complete and charge flows; an open switch breaks the path and current stops.
- Current (I) — rate of flow of charge, I = Q÷t, measured in amperes (A). Conventional current flows from + to − outside the cell.
- Potential difference / Voltage (V) — work done per unit charge to move charge between two points, measured in volts (V).
- Resistance (R) — opposition to current flow, measured in ohms (Ω).
Charge: Q = I × t (coulombs)
1 ampere = 1 coulomb per second.
1 volt = 1 joule per coulomb.
It helps to picture a circuit as a water system. The cell is the pump that raises water to a height; voltage is like the pressure difference it creates; current is the rate at which water flows; and resistance is like a narrow pipe that throttles the flow. This analogy is not perfect, but it explains why a stronger cell (more voltage) drives a larger current and why a thinner wire (more resistance) reduces it.
Current is the same everywhere in a single unbranched (series) loop because charge cannot pile up or disappear — it is conserved. At a junction, the current entering equals the current leaving, which is the basis of Kirchhoff's current law.
Ohm's law: the master relation
At constant temperature, the current through a conductor is directly proportional to the potential difference across it. This gives the single most used formula in the chapter.
V = I × R
From this: I = V÷R and R = V÷I
Units: V in volts, I in amperes, R in ohms (Ω).
A graph of V against I for an ohmic conductor is a straight line through the origin; its slope equals the resistance. Materials that obey this (most metals at fixed temperature) are called ohmic; devices like diodes and filament bulbs are non-ohmic because their resistance changes with conditions.
Resistance itself depends on the material and shape of the conductor: R = ρL÷A, where ρ is resistivity, L the length and A the cross-sectional area. So a long thin wire has high resistance and a short thick wire has low resistance — a favourite CDS one-liner.
If the temperature rises, the resistance of a metal increases. That is why a glowing bulb filament draws less current when hot than the cold-resistance calculation suggests.
Series circuits: one path for current
In a series connection the components are joined end to end, forming a single path. The same current flows through every element, while the source voltage is shared among them.
Series resistance adds directly:
Rs = R1 + R2 + R3 + …
Current I is the same in every component.
Total voltage V = V1 + V2 + V3 + …
- The equivalent resistance is larger than the biggest individual resistor.
- If one component breaks (e.g. one bulb fuses), the whole circuit goes dead — like old-style fairy lights.
- Voltage divides in the ratio of the resistances: the larger resistor gets the larger share.
Thinking series bulbs glow brighter. Adding bulbs in series raises total resistance, so current falls and each bulb glows dimmer, not brighter.
Parallel circuits: many paths for current
In a parallel connection the components are joined across the same two points, so each gets the full source voltage and the current splits between the branches.
Parallel resistance combines as reciprocals:
1÷Rp = 1÷R1 + 1÷R2 + 1÷R3 + …
For two resistors: Rp = (R1 × R2) ÷ (R1 + R2)
Voltage V is the same across every branch.
Total current I = I1 + I2 + I3 + …
- The equivalent resistance is smaller than the smallest individual resistor.
- Each appliance can be switched on or off independently — one failing does not stop the others.
- Every appliance gets the full mains voltage, which is why household wiring is always parallel.
Series adds resistance (R goes up); parallel adds the reciprocals (R goes down). This single contrast answers a large share of CDS circuit questions.
Electric power: P = VI and its variants
Electric power is the rate at which electrical energy is converted into other forms (heat, light, motion). Its SI unit is the watt (W), where 1 watt = 1 joule per second.
P = V × I
Using Ohm's law, also:
P = I² × R and P = V² ÷ R
1 kilowatt (kW) = 1000 W; 1 horsepower ≈ 746 W.
The three forms let you choose whichever fits the data. If you know current and resistance, use P = I²R; if you know voltage and resistance, use P = V²÷R.
A bulb marked 60 W, 230 V means it consumes 60 watts when run at 230 volts. From this you can find its resistance: R = V²÷P = 230²÷60 ≈ 882 Ω. A higher-wattage bulb at the same voltage therefore has lower resistance and draws more current.
For two bulbs in parallel on the mains, the higher-watt bulb glows brighter. For two bulbs in series, the lower-watt (higher-resistance) bulb glows brighter — a classic trick question.
Electrical energy and the kilowatt-hour
Energy is power multiplied by time. In SI units energy is in joules, but electricity bills use a larger commercial unit: the kilowatt-hour (kWh), called one unit of electricity.
Energy E = P × t
In joules: E = VIt (P in watts, t in seconds).
1 kWh = 1000 W × 3600 s = 3.6 × 106 J
Units consumed = power(kW) × time(hours).
To find a bill: total the kWh used by all appliances, then multiply by the tariff (rupees per unit). An appliance rated in watts running for hours each day is the standard set-up for these questions. The method is always the same — convert the power to kilowatts, multiply by the hours of use to get units, add up the units for all appliances, and finally multiply by the cost per unit.
This is also where examiners test understanding of efficiency. A 5-star rated appliance consumes fewer units for the same job, so it costs less to run over a month even if it is dearer to buy. An incandescent bulb wastes most of its energy as heat, whereas an LED of the same brightness draws far fewer watts and so consumes fewer kilowatt-hours.
The unit on an electricity meter is the kilowatt-hour, a unit of energy, not power. A 1000 W heater run for 1 hour consumes exactly 1 unit.
Heating effect and household circuits
When current flows through a resistance, electrical energy turns into heat — the heating effect of current, described by Joule's law: H = I²Rt. This is the working principle of heaters, geysers, electric irons, toasters and filament bulbs.
Household supply in India is about 220–230 V AC at 50 Hz. Wiring uses three wires: live (red/brown), neutral (black/blue) and earth (green). The earth wire is a safety path that carries leakage current to the ground and prevents shocks from metal casings.
- Appliances are connected in parallel so each gets full voltage and works independently.
- A fuse or MCB is placed in the live wire; it melts/trips if the current exceeds a safe value, breaking the circuit and preventing fire.
- Overloading (too many appliances) and short-circuiting (live touching neutral) both cause a dangerous current surge that the fuse is designed to interrupt.
Placing the fuse in the neutral wire. The fuse must be in the live wire so that, when it blows, the appliance is disconnected from the dangerous high potential.
Worked example: resistance, current and power
Two resistors of 6 Ω and 3 Ω are connected in parallel across a 12 V battery. Find (a) the equivalent resistance, (b) the total current from the battery, and (c) the power supplied.
Notice the equivalent resistance (2 Ω) is smaller than either resistor — the signature of a parallel combination. The branch currents add up to the total, confirming charge is conserved.
Previous-year style question
Q. An electric heater rated 1000 W is used for 2 hours daily. If the cost of electricity is ₹5 per unit, what is the cost of running it for 30 days?
Answer: Energy per day = power × time = 1 kW × 2 h = 2 kWh. For 30 days = 2 × 30 = 60 units. Cost = 60 × ₹5 = ₹300.
Always convert watts to kilowatts (divide by 1000) and minutes to hours before finding units. 1000 W = 1 kW — forgetting this is the commonest slip in bill questions.
Quick revision
- Ohm's law — V = IR, the basis of every numerical.
- Series — Rs = R1+R2+…; same current; resistance goes up.
- Parallel — 1÷Rp = Σ(1÷R); same voltage; resistance goes down.
- Power — P = VI = I²R = V²÷R, measured in watts.
- Energy — 1 unit = 1 kWh = 3.6×106 J; units = kW × hours.
- Home wiring — parallel; fuse in the live wire; heating effect H = I²Rt.
Frequently asked questions
Why are household appliances connected in parallel and not in series?
In parallel each appliance gets the full mains voltage and can be switched on or off independently, so one device failing does not stop the others. In series they would share the voltage and all would go off if one failed.
What is the difference between watt and kilowatt-hour?
The watt is a unit of power (the rate of using energy), while the kilowatt-hour is a unit of energy (power multiplied by time). Your electricity meter measures energy consumed in kilowatt-hours, called units.
Why does the equivalent resistance fall when resistors are added in parallel?
Adding parallel branches provides more paths for current to flow, just like widening a road eases traffic. More paths mean less overall opposition, so the equivalent resistance is always smaller than the smallest individual resistor.
Why is the fuse placed in the live wire?
So that when the fuse blows during overloading or a short circuit, it disconnects the appliance from the high-potential live wire, making the circuit safe. A fuse in the neutral wire would leave the appliance still connected to the live supply.
Of two bulbs in series, which glows brighter?
The bulb with the higher resistance (the lower-wattage one) glows brighter in series, because the same current flows through both and power dissipated is I²R, which is greater for the larger resistance. In parallel, the higher-wattage bulb is brighter.
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