State and apply Ohm's Law (V = IR)

WHAT is Ohm's Law?

The key word is proportional: double the voltage, and the current doubles — as long as $R$ stays constant (which needs constant temperature).

WHY is it true? (Derivation from first principles)

We don't just state $V=IR$ — we build it.

Formula Building V = IR from definitions

Step 1 — Define resistance. Resistance measures how hard it is to push current through something. The natural definition of "opposition to flow" is: $R \equiv \frac{V}{I}$ Why this step? Opposition = (how much push you needed) ÷ (how much flow you got). A big push giving tiny flow means big resistance.

Step 2 — Observe the experimental fact (Ohm's discovery). Ohm measured $V$ and $I$ for metal wires and found the ratio $V/I$ stays constant as you change $V$ . That constant is $R$ . Why this matters: If $R$ were changing with $V$ , we couldn't call it a simple law. The magic of ohmic materials is that $R$ is a fixed number.

Step 3 — Rearrange. Since $R = V/I$ is constant, multiply both sides by $I$ : $V = I R$ Why this step? This is now a predictive tool: give me any two quantities, I find the third.

HOW to apply it — the triangle trick

The three forms are just algebra on one equation:

$V = IR \qquad I = \frac{V}{R} \qquad R = \frac{V}{I}$

Mnemonic The VIR Triangle

Draw a triangle:

      V
     -----
    I  |  R

Cover the quantity you want:

Cover V → you see $I \times R$
Cover I → you see $V / R$
Cover R → you see $V / I$ "V sits on top (the boss), I and R share the bottom."

Figure — State and apply Ohm's Law (V = IR)

Worked Examples

Common Mistakes (Steel-manned)

Reading the V–I Graph

Active Recall

Recall Q: State Ohm's Law in words and symbols.

Current through an ohmic conductor is directly proportional to the voltage across it at constant temperature: $V = IR$ .

Recall Q: Rearrange for I and for R.

$I = V/R$ and $R = V/I$ .

Recall Q: What is the resistance if 4 A flows under 8 V?

$R = V/I = 8/4 = 2\ \Omega$ .

Recall Q: Why must temperature be constant?

Because heating changes R (more lattice vibration → more collisions → higher R), breaking the proportionality.

Recall Q: On a V–I graph of an ohmic resistor, what does the gradient represent?

The resistance $R$ .

Recall Feynman: explain to a 12-year-old.

Imagine pushing kids down a slide. Voltage is how steep you make the slide (the push). Current is how many kids reach the bottom each second. Resistance is how sticky/rough the slide is. Make it steeper (more voltage) and more kids slide down (more current). Make it stickier (more resistance) and fewer get down. The formula $V=IR$ just says: steepness = kids-per-second × stickiness.

80/20 — The 20% you must never forget

$V = IR$ and its two rearrangements.
Units: V, A, Ω — convert mA/kΩ first.
Ohmic ⇒ R constant ⇒ straight-line V–I graph, gradient = R.
V is across (parallel), I is through (series).

Flashcards

Ohm's Law equation

V = IR

Rearrange Ohm's Law for current

I = V/R

Rearrange Ohm's Law for resistance

R = V/I

Unit of resistance

Ohm (Ω)

Unit of current

Ampere (A)

Unit of potential difference

Volt (V)

What does "directly proportional" mean in Ohm's Law?

Doubling V doubles I when R is constant

Condition for Ohm's Law to hold

Constant temperature (ohmic conductor)

Convert 250 mA to amperes

0.25 A

Convert 4.7 kΩ to ohms

4700 Ω

Gradient of a V (y) vs I (x) graph

The resistance R

Shape of V–I graph for an ohmic resistor

Straight line through the origin

Shortcut: mA × kΩ = ?

Volts (the factors cancel)

Voltage is measured ___ a component; current ___ it

across; through

Find I: 12 V across 6 Ω

2 A

Find R: 9 V, 0.5 A

18 Ω

Why does R rise when a wire heats up?

Atoms vibrate more → more electron collisions → higher resistance

Is a filament lamp ohmic?

No — R increases as it heats, so V–I curve bends

Connections

Electric Current — the $I$ in the formula (charge flow per second)
Potential Difference (Voltage) — the $V$ , energy per unit charge
Resistance — the $R$ , plus resistivity and geometry
Series and Parallel Circuits — combining resistances, where V/I placement matters
Power in Circuits (P = VI) — combines with Ohm's Law to give $P = I^2R = V^2/R$
Non-ohmic Components — diodes, filament lamps where R varies

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, Ohm's Law bahut simple idea hai — bas ise paani ke pipe se samjho. Voltage (V) matlab kitna zyada "push" ya pressure hai, Current (I) matlab kitna paani (charge) actually beh raha hai per second, aur Resistance (R) matlab pipe kitna patla ya blocked hai. Formula hai $V = IR$ . Iska seedha matlab: push zyada karoge to flow zyada, aur pipe zyada blocked hoga to flow kam. Directly proportional ka matlab — voltage double karo to current bhi double ho jaata hai, jab tak R constant rahe.

Formula ko ratne ki zaroorat nahi, derive karo. Resistance ki definition hi $R = V/I$ hai (kitna push chahiye tha ÷ kitna flow mila). Ohm ne experiment se dekha ki metal wire mein ye ratio $V/I$ constant rehta hai — wahi constant R hai. Bas dono taraf $I$ se multiply karo aur $V = IR$ mil gaya. Microscopic level pe, electrons atoms se takraate rehte hain — yehi takrav resistance hai, aur temperature badhne pe atoms zyada hilte hain to R badh jaata hai. Isiliye "constant temperature" ki condition zaroori hai.

Apply karte waqt VIR triangle use karo: jo cheez chahiye use dhak do, baaki dikh jaayega. Sabse badi galti jo students karte hain — units convert nahi karte. mA ko A banao (÷1000), kΩ ko Ω banao (×1000), warna answer galat aayega. Ek shortcut yaad rakho: mA × kΩ = Volts seedha, kyunki 1000 wale factor cancel ho jaate hain.

Graph mein, agar V (y-axis) ko I (x-axis) ke against plot karo aur origin se seedhi line aaye, to wo ohmic resistor hai aur us line ka gradient hi R hota hai. Bulb ya diode ke liye line curved hoti hai — wahan R fixed nahi rehta, isliye unpe Ohm's Law ko fixed law maan ke mat chalna. Yeh chapter power ( $P=VI$ ) aur circuits se directly juda hai, isliye base strong rakho.

WHAT is Ohm's Law?

WHY is it true? (Derivation from first principles)

HOW to apply it — the triangle trick

Worked Examples

Common Mistakes (Steel-manned)

Reading the V–I Graph

Active Recall

80/20 — The 20% you must never forget

Flashcards

Connections

Concept Map

Hinglish (regional understanding)

Go deeper — visual, from zero

Test yourself — Electricity & Charge Basics

Connections