A 12 V battery drives a 4 ohm and a 6 ohm resistor in series. Find the current.

Step 1 — Combine the resistors

Resistors in series carry the same current, so their resistances add:

R_total = R₁ + R₂ = 4 Ω + 6 Ω = 10 Ω

Step 2 — Apply Ohm's law to the whole loop

I = V / R = 12 V / 10 Ω = 1.2 A

Step 3 — Check the voltage drops

4.8 V + 7.2 V = 12 V, which matches the battery — the loop rule is satisfied.

Why the current is the same everywhere

There is only one path, so charge has nowhere else to go. The larger resistor does not get less current; it takes a larger share of the voltage instead.