Electricity is just electric charge being pushed through a material . Ohm's Law is the exact bookkeeping of that pushing: it links how hard you push (voltage), how much charge actually moves (current), and how much the material fights back (resistance) — nothing more.
Before you can trust V = I R why the topic needs it . Read top to bottom; each idea stands on the one before it.
Definition Charge (symbolQ Charge is a property that some tiny particles carry. The particles that actually move in a wire are electrons , and each one carries a tiny fixed amount of negative charge.
Plain words: charge is "the stuff that electricity is made of."
Picture: think of charge as marbles . A wire is packed full of free electron-marbles.
We need charge because everything else is defined in terms of it . Voltage pushes charge; current is charge in motion; resistance opposes moving charge. No charge → nothing to talk about.
Intuition Why a wire has charge ready to moveIn a metal, the outer electrons of each atom are not glued down — they drift around freely, like a loose crowd of marbles between fixed atoms. That is what makes metal a conductor : it already has movable charge, just waiting for a push.
Definition Current (symbolI Current is how much charge flows past a point each second .
I = t Q
Q t Plain words: current is a flow rate — marbles-per-second, not a total.
Intuition Picture: count at the checkpointStand at one spot in the wire and count marbles crossing per second. That count is the current. A wide fast river and a thin trickle can carry the same total water over an hour — but current asks about this second , right now.
Why the topic needs I Ohm's Law is a statement about flow. I Electric Current for the full build.
Definition Potential difference / voltage (symbolV Voltage is the energy given to each unit of charge to push it from one point to another.
V = Q E
E Q Plain words: voltage is push-per-marble — how much shove each bit of charge receives.
Intuition Picture: the height of a slideVoltage is like the steepness of a slide . A steep slide (high voltage) gives each marble a strong push; a gentle slope (low voltage) barely nudges it. Voltage is always a difference between two points — the top of the slide versus the bottom. That is why we say "potential difference ."
Why the topic needs V V cause in Ohm's Law — the thing you control. Turn it up and, as we'll see, more current flows. See Potential Difference (Voltage) .
Common mistake "Voltage flows through the wire"Why it feels right: we say "voltage in the circuit," so it sounds like it travels.
The fix: voltage is measured across two points (like measuring a height difference), not through something. Only current flows. Voltage is the push; current is the movement.
Definition Resistance (symbolR Ω Resistance is how strongly a material opposes the flow of charge .
Plain words: how "clogged," narrow, or sticky the path is.
Picture: a narrow, gravel-filled pipe slows water even under strong pressure. A high-resistance wire slows charge even under strong voltage.
Intuition Where resistance comes from (the marble view)As electron-marbles drift forward, they keep bumping into the fixed atoms of the metal. Each bump steals a little speed. More bumps → harder to get through → higher resistance. This is the microscopic reason resistance exists at all.
Why the topic needs R R material's personality . Given the same push, a big-R
Now — and only now — every symbol in V = I R
Symbol
Plain words
Picture
Unit
V push per charge
steepness of the slide
volt (V)
I charge flow per second
marbles-per-second past a point
ampere (A)
R opposition to flow
narrowness / gravel in the pipe
ohm (Ω
Intuition Reading the equation like a sentenceV = I R "the push equals the flow multiplied by the fight-back."
Want more flow (I R V
Same push but more clogging? Less flow gets through.
Every worked example in the parent note is just this sentence, rearranged.
Definition Directly proportional (∝ directly proportional when doubling one doubles the other, tripling one triples the other, and so on. We write I ∝ V
Picture: a straight line through the origin . If you plot V I ( 0 , 0 )
Intuition Why "through the origin" mattersThrough the origin means: no push → no flow (V = 0 ⇒ I = 0 misses the origin would mean flow with zero push, which is impossible here.
Why the topic needs proportionality: the whole point of calling V = I R law is that R R non-ohmic device, and the simple law breaks.
Definition The proportionality symbol∝ I ∝ V I V ∝ = R 1 I = R 1 V V = I R
Definition The "define" symbol≡ R ≡ I V ≡ this is a definition, true by choice, not something to prove . We decide to call V / I constant for metals.
Mnemonic The mA × kΩ shortcutBecause milli divides by 1000 and kilo multiplies by 1000, they cancel :
mA × k Ω = V 250 mA × 220 Ω 0.25 A × 220 Ω = 55 V 250 mA × 0.22 k Ω = 55 V
Current I equals charge per second
Voltage V equals energy per charge
Resistance R opposes flow
Ohms Law V equals I times R
Directly proportional straight line
Read it upward: charge is the raw ingredient; current and voltage are two different rates built from charge; resistance opposes the flow; and all three, plus the proportionality idea and correct units, meet at Ohm's Law.
Test yourself — cover the right side. If any answer is shaky, re-read that section before tackling the parent topic .
What does the symbol Q Electric charge, measured in coulombs (C)
What is current I The amount of charge flowing past a point each second (I = Q / t
What is the unit of current, and what does 1 A equal? The ampere (A); 1 A = 1 coulomb per second
What is voltage V The energy given to each unit of charge (V = E / Q
Is voltage measured across or through a component? Across — it is a difference between two points
What flows through the wire — voltage or current? Current (charge in motion); voltage is only the push
What is resistance R How strongly a material opposes charge flow; measured in ohms (Ω
Where does resistance come from microscopically? Electrons colliding with the fixed atoms of the metal
What does "I ∝ V Doubling V I
Why must a proportional graph pass through the origin? No push means no flow: V = 0 ⇒ I = 0
What does the symbol ≡ "Is defined as" — true by choice, not by proof
Convert 250 mA to amperes 0.25 A
Convert 4.7 kΩ to ohms 4700 Ω
Why do mA and kΩ cancel to give volts? milli (÷1000) and kilo (×1000) cancel, leaving base units
