Every NDA paper asks something about current electricity — a bulb's wattage, two resistors in series, or why a fuse melts. The good news? This chapter runs on a handful of formulas you can master in one sitting. The Cavalier breaks it down into plain language, quick tricks and exam-style practice so you never lose these easy marks.
Why Current Electricity Matters in NDA
Open any NDA General Ability Test physics section and you will spot 3–5 questions built on electricity. They are rarely tough — they test whether you remember the right formula and can plug in numbers quickly.
Topics that repeat year after year include Ohm's law, series and parallel resistances, the heating effect, electric power and energy, and the practical role of fuses. Master these and you bank guaranteed marks while others struggle with optics or modern physics.
Current electricity questions are calculation-light. Memorise the eight core formulas in this page and you can finish each question in under 30 seconds.
Electric Charge and Electric Current
Matter is made of atoms, and atoms carry charged particles — negatively charged electrons and positively charged protons. When electrons flow through a conductor like a copper wire, we call that flow an electric current.
Defining current
Electric current is the rate of flow of charge. If a charge Q passes a point in time t:
I = Q ÷ t
Current (I) is measured in amperes (A), charge (Q) in coulombs (C), time (t) in seconds (s).
1 ampere = 1 coulomb per second.
One coulomb is the charge of about 6.25 × 1018 electrons. The charge on a single electron is 1.6 × 10−19 C.
Conventional current is taken in the direction of positive charge flow — opposite to the actual direction in which electrons move. Don't mix the two up in diagrams.
Potential Difference and the Cell
For current to flow, something must push the electrons. That push is the potential difference (voltage) supplied by a cell or battery.
Potential difference between two points is the work done to move a unit charge from one point to the other:
V = W ÷ Q
Voltage (V) is measured in volts. 1 volt = 1 joule per coulomb.
A cell converts chemical energy into electrical energy, maintaining the voltage that drives current around a circuit. The voltage measured across the cell when no current flows is its EMF (electromotive force).
Measuring instruments
- An ammeter measures current and is connected in series.
- A voltmeter measures potential difference and is connected in parallel.
An ideal ammeter has zero resistance; an ideal voltmeter has infinite resistance. This is a favourite one-line NDA question.
Ohm's Law — The Heart of the Chapter
Discovered by Georg Simon Ohm, this law links voltage, current and resistance. It states: at constant temperature, the current through a conductor is directly proportional to the potential difference across it.
V = I × R
Rearranged: I = V ÷ R and R = V ÷ I.
Resistance (R) is measured in ohms (Ω).
On a V–I graph, an ohmic conductor gives a straight line through the origin. The slope of that line equals the resistance.
Cover the quantity you want in the triangle V over I×R: cover V to get I×R, cover I to get V÷R, cover R to get V÷I. A 5-second memory trick for the exam hall.
Conductors that obey Ohm's law (metals, at fixed temperature) are called ohmic. Devices like diodes and filament bulbs are non-ohmic because their V–I graph curves.
One thing examiners love to test is the condition at constant temperature. If a wire heats up while current flows, its resistance changes and the simple straight-line relationship no longer holds perfectly. That is exactly why a glowing filament bulb is non-ohmic — its temperature, and hence its resistance, keeps rising as more current passes through it.
What Decides a Conductor's Resistance
Resistance opposes the flow of current. Four physical factors control it:
- Length (L): resistance is directly proportional to length. A longer wire has more resistance.
- Area of cross-section (A): resistance is inversely proportional to thickness. A thicker wire has less resistance.
- Material: captured by resistivity (ρ), a property of the material itself.
- Temperature: for metals, resistance rises as temperature rises.
R = ρ × (L ÷ A)
Resistivity ρ is measured in ohm-metre (Ω·m). It does not depend on the size or shape of the wire — only on the material and temperature.
Conductors, insulators and semiconductors
- Conductors (copper, silver, aluminium): very low resistivity.
- Insulators (rubber, glass, dry wood): extremely high resistivity.
- Semiconductors (silicon, germanium): in between, and their resistance falls with rising temperature.
Resistance (R) depends on the wire's dimensions; resistivity (ρ) does not. Cut a wire in half and each piece has half the resistance, but the resistivity stays exactly the same.
Resistors in Series
Resistors are in series when they are joined end to end so the same current flows through each.
Total resistance: Rs = R1 + R2 + R3 + …
The combined resistance is always larger than the biggest individual resistor.
Rules for series
- Current is the same through every resistor.
- Voltage divides across the resistors (larger R gets larger share).
- Total voltage = sum of individual voltages: V = V1 + V2 + V3.
In old decorative light strings, all bulbs are in series — so if one bulb fails, the whole string goes dark. That is the practical signature of a series circuit.
Resistors in Parallel
Resistors are in parallel when both ends are joined to the same two points, so each gets the same voltage but current splits between them.
Total resistance: 1 ÷ Rp = 1÷R1 + 1÷R2 + 1÷R3 + …
The combined resistance is always smaller than the smallest individual resistor.
For just two resistors in parallel, a quick shortcut is:
Rp = (R1 × R2) ÷ (R1 + R2) — the "product over sum" rule. Two equal resistors R in parallel simply give R÷2.
Rules for parallel
- Voltage is the same across every resistor.
- Current divides (smaller R takes more current).
- Household wiring uses parallel connection so each appliance gets full mains voltage and works independently.
Heating Effect of Electric Current
When current flows through a resistance, electrical energy turns into heat. This is Joule's heating effect, the principle behind heaters, irons, geysers and bulbs.
Heat produced: H = I² × R × t (in joules)
Because V = IR, this can also be written as H = VIt or H = (V²÷R)t.
This is why a heater coil is made of nichrome — it has high resistivity and a high melting point, so it glows red-hot without melting.
The electric fuse
A fuse is a safety device: a thin wire of low melting point placed in series with an appliance. If the current rises dangerously high, the heating effect melts the fuse wire and breaks the circuit, protecting the appliance and preventing fire.
Heat depends on the square of current (I²), not just I. Doubling the current produces four times the heat — a frequently tested point.
Electric Power and Energy
Electric power is the rate at which electrical energy is consumed or produced.
P = V × I
Using Ohm's law, also: P = I²R and P = V² ÷ R.
Power is measured in watts (W). 1 watt = 1 joule per second. 1000 W = 1 kilowatt (kW).
Electrical energy and the "unit"
Energy = power × time. The electricity bill is charged in kilowatt-hours (kWh), commonly called a "unit".
1 unit = 1 kWh = 1000 watt × 1 hour = 3.6 × 106 joules. A 100 W bulb burning for 10 hours uses exactly 1 unit.
A bulb marked "60 W, 220 V" means it consumes 60 watts when connected to 220 volts. From P = V²÷R you can find its resistance.
A useful insight for the exam: a bulb with a lower wattage rating actually has a higher resistance. A 40 W bulb resists current more than a 100 W bulb on the same supply, because less power means less current flows through it. Students often guess the opposite, so keep this fact firmly in mind.
Worked Example
Two resistors of 6 Ω and 3 Ω are connected in parallel across a 12 V battery. Find (a) the total resistance, (b) the total current drawn from the battery, and (c) the power dissipated.
So the combination behaves like a single 2 Ω resistor, draws 6 A, and dissipates 72 watts of power. Notice how the parallel resistance (2 Ω) is smaller than either resistor — exactly as the rule predicts.
As a quick check, you can also find the current through each branch separately. The 6 Ω resistor carries 12÷6 = 2 A, and the 3 Ω resistor carries 12÷3 = 4 A. These add up to 6 A, matching the total current we found. Whenever a numerical lets you cross-verify like this, do it — it catches careless slips in the exam hall and builds real confidence with circuits.
Previous-Year Style Practice
Q. An electric bulb is rated "220 V, 100 W". What is the resistance of its filament?
Answer: Using P = V² ÷ R, we get R = V² ÷ P = (220 × 220) ÷ 100 = 48400 ÷ 100 = 484 Ω.
NDA loves rating-plate questions like this because they combine the power formula with a small calculation. The same logic finds the current too: I = P÷V = 100÷220 ≈ 0.45 A.
If a question gives you any two of voltage, current, resistance and power, you can always find the other two — all four are linked through V = IR and P = VI.
Quick Revision
- Current: I = Q÷t, unit ampere; conventional current is opposite to electron flow.
- Ohm's law: V = IR — the master formula.
- Resistance: R = ρL÷A; rises with length, falls with thickness.
- Series: Rs = R1+R2+… (adds up); same current everywhere.
- Parallel: 1÷Rp = 1÷R1+1÷R2+… (reduces); same voltage everywhere.
- Heating: H = I²Rt; fuse melts to protect circuits.
- Power: P = VI = I²R = V²÷R; energy in kWh (1 unit = 3.6×106 J).
If you memorise just two relations — V = IR and P = VI — you can derive almost every other formula in this chapter on the spot.
Frequently asked questions
What is the difference between resistance and resistivity?
Resistance (R, in ohms) depends on the wire's length, thickness and material. Resistivity (ρ, in ohm-metre) is a property of the material alone and does not change with the wire's size or shape, only with temperature.
Why is household wiring done in parallel and not in series?
In parallel each appliance receives the full mains voltage and works independently, so switching one off does not affect the others. In series, all devices would share the voltage and one failure would cut power to everything.
Why does the heating effect depend on the square of current?
Heat is given by H = I²Rt, so doubling the current produces four times the heat. This square dependence is why even small overloads can rapidly overheat wires and trip a fuse.
What does a bulb rated '60 W, 220 V' actually mean?
It means the bulb consumes 60 watts of power when connected to a 220 volt supply. From these ratings you can find its resistance using R = V²÷P and its working current using I = P÷V.
Is current the flow of electrons or positive charge?
Physically, current in a metal is the flow of electrons (negative charge). But by convention, the direction of current is taken as the direction in which positive charge would move — opposite to the electron flow.
How many marks can Current Electricity fetch in NDA?
Typically 3 to 5 marks appear from this chapter in the General Ability Test physics section, mostly as direct formula-based or rating-plate questions, making it one of the highest-yield, easiest topics to prepare.
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