Electricity & Current – NDA Physics Notes

Press a light switch. The bulb glows instantly, before you have even lifted your finger.

Did electrons race from the battery to the bulb in that fraction of a second? No. Understanding why is the key to understanding electricity.

Electric charges are already present throughout the conducting wire. The battery does not create or send electrons. It creates a potential difference (a kind of electrical pressure) across the circuit. This potential difference establishes an electric field almost instantly throughout the entire conductor. Under this field, electrons begin drifting slowly in one direction. But the electrical effect of that field reaches the bulb at nearly the speed of light.

1. Electric Charge: Properties

Electric charge is the fundamental property of matter that causes particles to attract or repel each other. Every electron carries a negative charge. Every proton carries a positive charge of equal magnitude.

Property 1: Conservation: Charge cannot be created or destroyed in an isolated system. The total charge in any isolated process remains constant.

Property 2: Quantisation: Any charge on a body is always an integer multiple of the elementary charge e = 1.6 × 10⁻¹⁹ C. A charge of 3.5e is impossible. Charge comes in whole multiples of e.

Property 3: Algebraic addition: Positive and negative charges can be added algebraically. +5 C and −3 C give a total of +2 C.

The NOT a property: “Charges can be created and destroyed in an isolated system.” This violates conservation. [NDA 2025-I]

2. Charging by Friction, Induction, and Contact

Charging by Friction

When a rod is rubbed with wool, electrons transfer from one material to the other. Positive charges (protons) never transfer. They are fixed inside atomic nuclei. [NDA 2017-I]

When an insulating rod is rubbed with wool and acquires a negative charge: electrons move from the wool to the rod. The rod gains electrons (becomes negative). The wool loses electrons (becomes positive). [NDA 2017-I]

Charging by Induction

When a positively charged insulating rod is brought near a neutral metal ball: electrons in the metal are attracted toward the near end (making it negative). The far end loses electrons (becomes positive). The net charge of the ball is still zero. Only the distribution has changed. The ball is attracted to the rod because the near negative end is closer to the rod than the far positive end. [NDA 2011-II]

What Charges an Insulator

An insulator can be charged by static electricity (friction, induction by contact). Current electricity, magnetic fields, and gravitational fields do not charge insulators. [NDA 2019-I]

Walking on Carpet: Electrostatic Discharge

Walking on a woollen carpet causes charge transfer to the body by friction. When the finger approaches a metallic door handle, the accumulated charge discharges, producing a spark and electric shock. This is electrostatic discharge, not a chemical or thermal reaction. [NDA 2015-I]

3. Coulomb’s Law

Coulomb’s Law gives the force between two point charges:

F = kq₁q₂ / r²

F = force between the charges (N). k = 9 × 10⁹ N m² C⁻². q₁, q₂ = magnitudes of the two charges (C). r = separation between them (m). Force is inversely proportional to the square of the distance. When separation doubles (5 cm → 10 cm): F_new = F/(2)² = F/4. The force reduces to one-fourth. [NDA 2012-I]

Sign of the Force: A positive force (repulsion) exists when both charges have the same sign, both positive or both negative. [NDA 2022-I] Like charges: repel. Unlike charges: attract.

Newton’s Third Law in Electrostatics: The force body A exerts on body B equals the force body B exerts on body A, with equal magnitude and opposite direction. The force ratio between two interacting charges is always 1:1.

4. Electric Field and Field Lines

The electric field E at a point is the force per unit positive test charge placed at that point. It is a vector quantity.

Electric Field Inside a Hollow Conductor

Inside a hollow conducting shell, the electric field is zero everywhere. This is the principle of electrostatic shielding. [NDA 2010-II | NDA 2017-I]

Electric Field Lines from a Positive Conductor

Field lines from an isolated positively charged conducting sphere are directed radially outward and perpendicular to the surface. [NDA 2022-I] Field lines cannot be tangential to the surface, as that would imply a component of force along the surface, causing current to flow, which contradicts electrostatic equilibrium.

5. Electric Potential and Potential Difference

Electric potential V at a distance r from a point charge q:

V = kq / r

If charge is doubled AND distance is doubled: V_new = k(2q)/(2r) = kq/r = V unchanged. [NDA 2011-II]

Potential Difference: V = W/Q. W = 24 J, Q = 2 C: V = 24/2 = 12 V. [NDA 2025-I]

Energy Gained by an Electron: An electron (charge e = 1.6 × 10⁻¹⁹ C) accelerated through V = 1 kV gains: E = eV = 1.6 × 10⁻¹⁹ × 1000 = 1.6 × 10⁻¹⁶ J. [NDA 2018-II]

Quantity	Meaning	SI Unit	Depends On
Charge	Quantity of electricity	Coulomb (C)	Number of electrons (quantised)
Current	Rate of flow of charge	Ampere (A)	Charge passing per second: I = Q/t
Voltage (PD)	Energy transferred per unit charge	Volt (V = J C⁻¹)	Potential difference between two points
EMF	Energy supplied per unit charge by the source	Volt (V)	Internal characteristics of the source (battery)
Resistance	Opposition to charge flow	Ohm (Ω)	Material, length, area, temperature
Resistivity	Material’s opposition per unit geometry	Ohm-metre (Ω m)	Material and temperature ONLY

6. Capacitor: Parallel Plate

A capacitor stores electric charge and energy. The simplest form is two parallel conducting plates separated by a distance d.

C = ε₀A / d

C = capacitance (Farad). ε₀ = 8.85 × 10⁻¹² F m⁻¹. A = area of each plate (m²). d = separation between plates (m).

Action	Effect on C	Why
Double plate area A alone	C doubles	C ∝ A: larger area captures more charge
Halve plate separation d alone	C doubles	C ∝ 1/d: closer plates have stronger field
Double both A and d	C unchanged	Effects cancel exactly: (2A)/(2d) = A/d
Double d alone	C halves	C ∝ 1/d: larger separation weakens field

Only doubling A alone and halving d alone successfully double C. [NDA 2010-II]

7. Van de Graaff Generator

A Van de Graaff generator is used to accelerate charged particles (ions, electrons) to high kinetic energies. [NDA 2014-I] It builds up a very high electrostatic potential on its dome. It does not generate large currents, high-frequency voltages, or an electric field (in the sense that question tests). Its purpose is particle acceleration for physics experiments.

8. Resistance and Resistivity

Why Resistance Exists

When electrons move through a conductor, they collide with atoms in the metal lattice. Each collision slows them down. The more frequent the collisions, the greater the opposition to flow. This opposition is electrical resistance. Three factors increase resistance: longer wire (more atoms → more collisions), thinner wire (fewer paths → more congestion), different material (some materials have more tightly bound electrons).

The Resistance Formula

R = ρL / A

R = resistance (Ω). ρ = resistivity (Ω m). L = length of the wire (m). A = cross-sectional area (m²).

Resistivity: The Material Property

★ IMPORTANT Resistivity (ρ), also called specific resistance, is a property of the material ONLY. It does NOT depend on the length or cross-sectional area of the wire. [NDA 2010-I | NDA 2016-II | NDA 2022-I | NDA 2025-I]

Changing only the length of a copper wire: resistance doubles (R = ρL/A increases with L), but resistivity remains exactly the same. [NDA 2025-I]

Two copper wires A and B (same material, lengths l and 2l, same area): resistivity of A equals resistivity of B → ratio = 1:1. [NDA 2011-II]

Conductivity and Resistivity: Conductivity σ = 1/ρ. The product σρ = 1 for all conductors. This is an identity, not a variable. [NDA 2015-I]

Insulators and Free Electrons: Insulators do not contain zero electrons. They have electrons, but those electrons are tightly bound to atoms and cannot drift freely. [NDA 2017-I] Current in a metal is carried by free electrons. [NDA 2024-I]

Property	Resistance (R)	Resistivity (ρ)
Definition	Opposition to charge flow in a specific conductor	Opposition per unit geometry: material property
Formula	R = ρL/A	ρ = RA/L
SI unit	Ohm (Ω)	Ohm-metre (Ω m)
Depends on length L?	YES: R ∝ L	NO: material property only
Depends on area A?	YES: R ∝ 1/A	NO: material property only
Depends on material?	YES (via ρ)	YES: primarily
NDA confusion	Confused with resistivity	Commonly stated to depend on L and A: WRONG

9. Resistance vs Wire Dimensions: Six Problem Types

Every NDA problem involving wire resistance maps to one of six patterns. All use R = ρL/A from first principles.

Type 1: Same material, same length, different area: Wire B has double the cross-section of wire A (same material, same length). R_B = ρL/(2A) = R_A/2. Doubling area halves resistance. [NDA 2012-I]

Type 2: Different length and radius (same material): Wire A: radius r, length l → R_A = ρl/(πr²). Wire B: radius 2r, length l/2 → R_B = ρl/(8πr²) = R_A/8. Wire B has one-eighth the resistance of wire A. [NDA 2019-I]

Wire A: radius 2r (r_A = 2r_B). Wire B: radius r. Same material, same length. R_A/R_B = r_B²/r_A² = 1/4. R_A : R_B = 1:4. [NDA 2014-I]

Type 3: Same material, same length, different area: power dissipation: Wires A (radius r, length l) and B (radius 2r, length 2l), same voltage V. R_A = ρl/(πr²). R_B = ρ(2l)/(π(2r)²) = R_A/2. Power P = V²/R. Wire A dissipates half the power of wire B. [NDA 2019-I]

Type 4: Different dimensions, full ratio: Wire A: length l, area A. Wire B: length 2l, area A/2 (same material). R_B/R_A = 4. Wire B has four times the resistance of wire A. [NDA 2010-II]

Type 5: Wire cut into equal parts, reconnected in parallel: Wire of resistance R cut into n equal parts → each part R/n. n parts in parallel: R_eq = R/n².

20 Ω cut into 2 parts (each 10 Ω), parallel: R_eq = 10/2 = 5 Ω   [NDA 2020-I & II]

50 Ω cut into 5 parts (each 10 Ω), parallel: R_eq = 10/5 = 2 Ω   [NDA 2022-I]

Type 6: Replacing a network with an equivalent wire: Three wires each of length L, area A, resistivity ρ: two in parallel (R/2), in series with the third (3R/2). Replacement wire must satisfy L₁ = 3L, A₁ = 2A (since 3L/2A = 3L/2A). [NDA 2026-I]

10. Stretching a Wire: The n² Rule

When a wire is stretched, its volume is conserved. This is the most tested single calculation type in NDA Physics.

If length increases to nL: A_new = A/n  (volume = LA = nL × A/n)

R_new = ρ(nL)/(A/n) = n²ρL/A = n²R

★  IMPORTANT Stretching a wire to n times its length multiplies its resistance by n². [NDA 2012-I | NDA 2015-II | NDA 2023-I]

Stretch Factor (n)	New Length	New Area	New Resistance
n = 2 (doubled)	2L	A/2	4R
n = 10	10L	A/10	100R
n in general	Nl	A/n	n²R

10 Ω wire stretched to 10 times its length: R_new = (10)² × 10 = 1000 Ω. [NDA 2012-I]

Wire of x Ω stretched to double its length: R_new = 4x Ω. [NDA 2015-II] In circuit with same V: new current = original current/4. [NDA 2023-I]

11. Ohm’s Law

For many materials, the current through a conductor is proportional to the potential difference across it, provided physical conditions remain constant.

V = IR

V = potential difference (V). I = current (A). R = resistance (Ω). Ohm’s Law defines resistance. It does not independently define current or voltage. [NDA 2013-I]

A device obeys Ohm’s Law when its resistance remains constant regardless of the magnitude or polarity of applied voltage. On an I-V graph, a straight line through the origin confirms Ohm’s Law.

When Ohm’s Law Does NOT Apply: Not all materials are ohmic. Semiconductors, diodes, and many electronic devices do not obey Ohm’s Law. [NDA 2019-II] The incorrect statement: “All homogeneous materials obey Ohm’s Law irrespective of field strength.” A device conducting in one polarity only behaves as a p-n junction diode. [NDA 2014-I]

12. Series and Parallel Resistance Combinations

Series Circuit

In a series circuit, all components are connected in a single chain. There is only one path for current to flow. The same current flows through every component. Voltage distributes among components in proportion to their resistance. Example: decorative lights, where when one bulb fails, all go off.

R_series = R₁ + R₂ + R₃ + …

Equivalent series resistance is always greater than the largest individual resistance.

Parallel Circuit

In a parallel circuit, components are connected across the same two points, giving multiple paths for current. The same voltage appears across every branch. Current divides among branches. Example: household wiring, where appliances operate independently at full voltage.

1/R_parallel = 1/R₁ + 1/R₂ + 1/R₃ + …

Equivalent parallel resistance is always less than the smallest individual resistance. [NDA 2016-I]

Standard NDA-Tested Patterns

Three equal resistors r in parallel: 1/R_eq = 3/r → R_eq = r/3. [NDA 2010-I | NDA 2021-I | NDA 2021-II | NDA 2025-I]

Series:Parallel ratio for three equal r: 3r/(r/3) = 9. Series is 9× the parallel value. [NDA 2016-II | NDA 2021-II | NDA 2025-I]

Three r: series = 90 Ω → each = 30 Ω. Parallel: R_eq = 30/3 = 10 Ω   [NDA 2015-II]

1 Ω, 2 Ω, 3 Ω in series, 9 V: R = 6 Ω, I = 1.5 A. Voltage across 3 Ω: 4.5 V   [NDA 2011-II]

Two equal R parallel, 12 V, 100 mA: R_eq = 120 Ω, R = 240 Ω   [NDA 2020-I & II]

Two R parallel then series with one R: total = 3R/2   [NDA 2023-I]

13. Mixed Resistance Networks: Worked Examples

Series-Parallel Combination: 5 Ω and 7 Ω in series = 12 Ω. Then in parallel with 36 Ω: 1/R = 1/12 + 1/36 = 4/36. R_eq = 9 Ω. [NDA 2024-II]

12 V Battery, 24 Ω Bulb: I = V/R = 12/24 = 0.5 A. [NDA 2016-I]

Parallel with Resistors R₁ and R₂ (Same Material, Same Thickness): R₁ (length L₁) and R₂ (length 2L₁) → R₂ = 2R₁. In parallel: R_total = 2R₁/3. [NDA 2022-I]

Heater at Different Voltages: At 220 V draws 0.5 A: R = 440 Ω. At 120 V: I = 120/440 ≈ 0.27 A. [NDA 2023-II]

Heat Ratio: Parallel vs Series (Same Wires, Same Voltage): Two identical R. Parallel: R_eq = R/2, P = 2V²/R. Series: R_eq = 2R, P = V²/2R. Ratio = 4:1. Heat in parallel is 4× heat in series. [NDA 2025-I]

14. Kirchhoff’s Laws

Kirchhoff’s Current Law (KCL): The sum of all currents entering a junction equals the sum of all currents leaving. This is a statement of conservation of charge.

Kirchhoff’s Voltage Law (KVL): The sum of all EMFs and potential drops around any closed loop equals zero. This is a statement of conservation of energy applied to electric circuits. [NDA 2019-II]

15. Measuring Instruments: Ammeter, Voltmeter, Galvanometer

Ammeter: Measures electric current. Always connected in SERIES, in line with the component. Must have very LOW resistance so it does not significantly alter the current. [NDA 2020-I & II | NDA 2025-I]

Voltmeter: Measures potential difference between two points. Always connected in PARALLEL, across the component. Must have very HIGH resistance so it draws negligible current. [NDA 2025-I]

The incorrect statement: “Voltmeter has low resistance and ammeter has high resistance.” This is the exact opposite of reality. [NDA 2025-I]

Galvanometer: Detects the presence and direction of electric current. [NDA 2020-I & II | NDA 2021-II] Can detect small currents, not measure large ones. A galvanometer is not an ammeter.

Generator vs Galvanometer: A generator produces electric current. A galvanometer detects it. [NDA 2021-II]

16. Electrical Power: Three Equivalent Formulas

Electrical power is the rate at which electrical energy is converted into other forms. When a current I flows through a potential difference V:

P = VI   →   P = I²R   →   P = V²/R

All three forms are equivalent. The product VI represents thermal power dissipated, not resistance, not total heat, and not rate of change of resistance. [NDA 2013-I]

★  IMPORTANT IR² is NOT a valid power formula.   [NDA 2021-I | NDA 2022-II] Valid forms: VI, I²R, V²/R: and nothing else.

Expression	Valid Power Formula?	Reason
P = VI	YES	Power = current × voltage
P = I²R	YES	Derived from P=VI and V=IR
P = V²/R	YES	Derived from P=VI and I=V/R
P = IR²	NO	Incorrect: not physically valid as power
P = I²/R	NO	Wrong: has wrong units

60 W bulb at 240 V: I = P/V = 60/240 = 0.25 A.   [NDA 2022-I]

220 V generator, current 600 mA = 0.6 A: P = 220 × 0.6 = 132 W.   [NDA 2022-II]

220 V, 80 W bulb: R = V²/P = (220)²/80 = 605 Ω. At 110 V: P_new = (110)²/605 = 20 W (one-quarter).   [NDA 2023-I]

I per 60 W bulb at 240 V = 0.25 A. With 4 A fuse: max bulbs = 4/0.25 = 16 bulbs.   [NDA 2010-I]

17. Joule’s Law of Heating

When current flows through a resistor, electrical energy converts to heat:

H = I²Rt

H = heat generated (J). I = current (A). R = resistance (Ω). t = time (s).

At constant R and t: H ∝ I². Doubling the current quadruples the heat. [NDA 2016-I]

I = 1 A → H = 2000 J. I = 2 A → H = 4 × 2000 = 8000 J.

Cutting a Coil in Half: Heating coil cut in half, only one half used: resistance becomes R/2. At the same voltage V: P_new = V²/(R/2) = 2V²/R = 2P. Heat generated doubles when the coil resistance halves. [NDA 2010-II]

Temperature Rise in Water: The rise in temperature depends on all three: supply voltage (determines current through R), current (determines heat H = I²Rt), and time (more time = more heat). [NDA 2019-II]

18. Electrical Energy and Cost

1 unit = 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J

Cost = P (in kW) × t (in hours) × rate (₹ per kWh)

100 W lamp for 10 hours = 100 × 10 = 1000 Wh = 1 kWh = 1 unit.   [NDA 2011-II]

5 kW refrigerator, 10 hours/day for 30 days: energy = 5 × 10 × 30 = 1500 kWh. Cost at ₹4/unit = ₹6,000.   [NDA 2020-I & II]

A bulb: filament resistance 200 Ω, current 2 A, on for 10 h, rate ₹5/unit. Converts 20% of power to light. Power = I²R = 4 × 200 = 800 W = 0.8 kW. Light power = 0.2 × 0.8 = 0.16 kW. Energy for light = 0.16 × 10 = 1.6 kWh. Cost = 1.6 × ₹5 = ₹8.   [NDA 2024-II]

19. Fuse Wire and Short Circuit

Fuse Wire Properties

A fuse is a thin wire that protects circuits from excessive current. When current exceeds the rated value, the fuse wire heats up and melts, breaking the circuit. For this to work effectively, the fuse material must have:

High resistivity: so it heats up quickly even at moderate current (H = I²Rt, so for same I and t, higher R means more heat).

Low melting point: so it melts and breaks the circuit quickly before other components are damaged.

The fuse alloy of tin and lead satisfies both conditions. [NDA 2011-I | NDA 2013-I | NDA 2019-I]

The property of electric current used in a fuse is the heating effect, not chemical, magnetic, or optical effects. [NDA 2016-II]

Fuse Rating and Short Circuit

A fuse rated 16 A will break (blow) when current exceeds 16 A. [NDA 2012-II]

Short circuit occurs when live and neutral wires touch directly, creating a near-zero resistance path. Current increases instantaneously and substantially. [NDA 2014-I | NDA 2020-I & II] The fuse melts to break the circuit.

20. Heating Element Materials

Heating elements (electric iron, water heater, room heater) must get hot and stay hot without melting. They require:

High resistivity: to generate substantial heat (H = I²Rt, so larger R means more heat for same I and t).

High melting point: to withstand the operating temperature without melting.

Nichrome (nickel-chromium alloy): the standard heating element material for electric irons. [NDA 2023-II] Tungsten: used for incandescent bulb filaments: extremely high melting point (3422°C). [NDA 2020-I & II]

Application	Required Resistivity	Required Melting Point	Material Used
Fuse wire	HIGH: generates heat fast	LOW: melts quickly to break circuit	Tin-lead alloy
Heating element (iron, heater)	HIGH: generates substantial heat	HIGH: must not melt in use	Nichrome
Bulb filament	HIGH: glows at high temperature	VERY HIGH: operates at ~2700°C	Tungsten
Connecting wire	LOW: minimal heat loss	Not critical	Copper, Aluminium

21. Lighting: LED, CFL, and Incandescent Bulbs

LED stands for Light Emitting Diode. [NDA 2018-II | NDA 2021-I] It is a semiconductor device that converts electrical energy to light very efficiently, far more efficiently than either CFL tubes or incandescent bulbs.

Correct power consumption order for equal light intensity (lowest to highest): LED < CFL < Fluorescent Tube < Incandescent Bulb   [NDA 2012-II]

Incandescent bulbs waste approximately 95% of energy as heat. LEDs convert about 80–90% of energy to light.

22. AC Supply in India

India’s domestic electricity supply is 220 V, 50 Hz alternating current. [NDA 2012-II] (Not 110 V: that is the US standard. Not 60 Hz: that is also the US standard.)

At 50 Hz, the current completes 50 full cycles per second. The current changes direction twice per cycle. So the direction changes 100 times per second = every 1/100 second. [NDA 2024-II | NDA 2022-I]

If AC frequency = 3 Hz: 3 cycles per second.   [NDA 2022-I]

23. Superconductors

When the electrical resistance of a material drops suddenly to zero below a certain critical temperature, the material is called a superconductor. [NDA 2011-I] Below the critical temperature, current flows without any resistance or energy loss. Applications: MRI machines, maglev trains, particle accelerators.

24. Lightning and Lightning Conductor

Lightning

Lightning is caused by charge separation in clouds. Negative charges accumulate at the base of a cloud. These induce positive charges on the ground below. When the electric field becomes strong enough, a discharge (lightning bolt) jumps between cloud and ground. [NDA 2024-II]

Lightning Conductor

A lightning conductor is a pointed metal rod at the top of a building connected to earth by a thick copper wire. It works by: (1) Sharp point creates corona discharge, ionising surrounding air and causing continuous small discharge that partially neutralises cloud charge. (2) Low-resistance path to earth: if lightning does strike, current flows through the copper conductor safely into the ground rather than through the building.

Statement 1 (creates electric field at tip) and Statement 3 (takes charge to earth) are correct. Statement 2 (distributes charge over building) is incorrect. [NDA 2015-II]

Aircraft Tyres: Conducting Rubber

Aircraft tyres are made of conducting rubber to safely discharge static electricity accumulated during flight to the ground on landing. [NDA 2022-I]

25. Advanced Circuit Analysis

Wheatstone Bridge

A Wheatstone bridge is a circuit of four resistors P, Q, R, S arranged in a diamond pattern with a galvanometer across the centre diagonal. The bridge is balanced (no current through galvanometer) when:

P/Q = R/S

Internal Resistance: Terminal Voltage

A real battery has an internal resistance r. When delivering current I, the terminal voltage is less than the EMF (E):

V_terminal = E − Ir

The drop Ir is the voltage lost inside the battery. At I = 0 (open circuit): V_terminal = E. Under load: V_terminal < E.

Drift Velocity

Electrons in a conductor are always in random thermal motion. When an electric field is applied, they gain a small average velocity in the field direction: called drift velocity (v_d). Drift velocity is typically about 0.1 mm per second, extremely slow. But the electric field effect propagates at nearly the speed of light, which is why the bulb glows instantly.

RMS and Peak Values of AC

V_rms = V₀ / √2 ≈ 0.707 V₀

India’s 220 V AC is the RMS value. The peak voltage = 220√2 ≈ 311 V.

Important Distinctions

Resistance vs Resistivity

Resistance is a property of a specific piece of wire. It depends on length, area, material, and temperature. Resistivity is a property of the material only. It depends on material and temperature, not length or area. Same material in any shape or size has the same resistivity.

Ammeter vs Voltmeter

Ammeter: measures current, connected in SERIES, LOW resistance. Voltmeter: measures voltage, connected in PARALLEL, HIGH resistance. Wrong way round in either case ruins the measurement or the meter.

Fuse vs Heating Element

Both need HIGH resistivity. Fuse needs LOW melting point (must melt fast to break circuit). Heating element needs HIGH melting point (must not melt during operation). Opposite melting point requirements.

EMF vs Terminal Voltage

EMF (E): total energy supplied per unit charge by the source, measured at zero current. Terminal voltage (V): potential difference between terminals when current flows, always less than EMF because of internal resistance drop Ir.

Series vs Parallel

Series: same current, different voltages, R_eq = sum (larger than any single R). Parallel: same voltage, different currents, R_eq < any individual R.

---