Physics › ⚡ Electricity & Magnetism

Current, Voltage & Circuits

Every circuit is just charge being pushed through a pipe of wire — once you can see the push, the flow, and the friction, the whole thing clicks.

High schoolAP Physics 2 level
💡
The big idea: A circuit is a story about charge in motion: voltage is the push, current is how much charge actually moves per second, and resistance is whatever slows that motion down. Ohm's law simply ties these three together, and once you add power and the two ways resistors can be wired — series and parallel — you can analyze almost any simple circuit by hand.
🎯 By the end, you'll be able to
  • explain what current, voltage, and resistance physically represent, using an intuitive flow analogy
  • apply Ohm's law (V = IR) to solve for current, voltage, or resistance in a simple circuit
  • calculate electrical power using P = VI and its equivalent forms, and connect it to energy use
  • find the equivalent resistance of resistors in series and in parallel, and predict how voltage and current split in each case
📎 You should already know
  • Electric Charge & Coulomb's Law
  • Electric Potential Energy & Voltage
  • Basic algebra (solving an equation for one variable)

Think of it like water in a pipe

Picture a garden hose connected to a water tower. The height of the tower creates pressure that pushes water through the hose. A narrow, kinked hose resists that flow more than a wide, straight one, so less water gets through per second.

An electric circuit works the same way. Voltage is the electrical "pressure" pushing charge around a loop of wire. Current is how much charge actually flows past a point each second. Resistance is anything in the wire that fights that flow — thin filaments, long wires, or components built specifically to resist. Nothing here is mysterious once you keep this picture in mind.

🔑 The three quantities are locked together

You almost never need to know current, voltage, and resistance independently — knowing any two tells you the third. That single relationship, discovered by Georg Ohm, is the workhorse of circuit analysis: more push (voltage) means more flow (current); more resistance means less flow for the same push.

\[ V = IR \]
Ohm's law: voltage (in volts) equals current (in amperes) times resistance (in ohms, \Omega).
\[ P = VI = I^2 R = \frac{V^2}{R} \]
Electrical power (in watts) — the rate at which the circuit converts electrical energy into heat, light, or motion. All three forms are the same equation, just substituted using Ohm's law.
\[ R_{series} = R_1 + R_2 + \cdots \qquad \frac{1}{R_{parallel}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots \]
Series resistors add directly; parallel resistors combine as reciprocals, so the parallel total is always smaller than the smallest individual resistor.
🎮 Interactive: Build a Circuit and Watch the Current Flow LIVE
Adjust the battery voltage and resistor values, switch between series and parallel wiring, and watch how current, voltage drops, and power respond in real time.

Why series adds and parallel divides

In a series circuit, there's only one path — every electron that flows through the first resistor must also flow through the second. Same current everywhere, but each resistor takes its own "bite" of the total voltage. Stack up resistors and you stack up the resistance, so the current for the whole loop drops.

In a parallel circuit, you've built multiple paths side by side. Each path feels the full battery voltage, but the current gets to split up and choose the easiest path (or several at once). Adding another parallel path gives current a new route, so the overall resistance to the battery actually goes down — it becomes easier, not harder, for the battery to push charge through.

📝 Worked example: A 12 V battery is connected to two resistors in series: \(R_1 = 4\,\Omega\) and \(R_2 = 2\,\Omega\). Find the current in the circuit and the voltage across each resistor.
  1. Series resistors add: \(R_{total} = R_1 + R_2 = 4\,\Omega + 2\,\Omega = 6\,\Omega\).
  2. Apply Ohm's law to the whole loop: \(I = \dfrac{V}{R_{total}} = \dfrac{12\text{ V}}{6\,\Omega} = 2\text{ A}\). This same current flows through both resistors.
  3. Find each resistor's voltage "bite" using \(V = IR\): \(V_1 = (2\text{ A})(4\,\Omega) = 8\text{ V}\), and \(V_2 = (2\text{ A})(2\,\Omega) = 4\text{ V}\).
  4. Check: \(V_1 + V_2 = 8\text{ V} + 4\text{ V} = 12\text{ V}\), matching the battery — the voltage drops must add up to the total push.
✓ Current = 2 A everywhere in the loop; \(V_1 = 8\text{ V}\), \(V_2 = 4\text{ V}\).
📝 Worked example: The same 12 V battery is now connected to \(R_1 = 6\,\Omega\) and \(R_2 = 3\,\Omega\) wired in parallel. Find the equivalent resistance, the current through each resistor, and the total power delivered.
  1. Combine using the parallel rule: \(\dfrac{1}{R_{total}} = \dfrac{1}{6} + \dfrac{1}{3} = \dfrac{1}{6} + \dfrac{2}{6} = \dfrac{3}{6} = \dfrac{1}{2}\), so \(R_{total} = 2\,\Omega\).
  2. Both resistors feel the full 12 V, so find each branch current with \(I = V/R\): \(I_1 = \dfrac{12\text{ V}}{6\,\Omega} = 2\text{ A}\), and \(I_2 = \dfrac{12\text{ V}}{3\,\Omega} = 4\text{ A}\).
  3. Total current from the battery is the sum of the branches: \(I_{total} = 2\text{ A} + 4\text{ A} = 6\text{ A}\) (matches \(I = V/R_{total} = 12/2 = 6\text{ A}\)).
  4. Total power: \(P = VI = (12\text{ V})(6\text{ A}) = 72\text{ W}\).
✓ \(R_{total} = 2\,\Omega\); \(I_1 = 2\text{ A}\), \(I_2 = 4\text{ A}\), total current = 6 A; total power = 72 W.
⚠️ Current isn't "used up"

A common trap is thinking current gets smaller as it passes through each component, like water being drained from a bucket. It doesn't. In a series loop, the same current flows into and out of every single element — what gets "used up" is energy (voltage drops as charge gives up energy to each resistor), not the charge itself. Also remember: these equations describe steady, simple resistive circuits. Real components can behave differently under changing signals or at extreme temperatures, but for the kind of circuits in this lesson, Ohm's law and the series/parallel rules are exact.

Check your understanding

1. Which equation correctly states Ohm's law?
Ohm's law relates voltage, current, and resistance as V = IR — voltage equals current multiplied by resistance.
2. A circuit has a 9 V battery connected to a single 3 Ω resistor. What is the current?
Rearranging Ohm's law: I = V/R = 9 V / 3 Ω = 3 A.
3. Two 4 Ω resistors are connected in parallel. What is the equivalent resistance?
1/R_total = 1/4 + 1/4 = 1/2, so R_total = 2 Ω. Parallel resistance is always less than either individual resistor.
4. In a series circuit powered by a fixed-voltage battery, you add a third resistor to the loop. What happens to the total current?
Adding a resistor in series increases the total resistance. Since voltage is fixed and I = V/R_total, a larger R_total means a smaller current.
✅ Key takeaways
  • Voltage is the push, current is the flow of charge, and resistance opposes that flow — tied together by Ohm's law, V = IR.
  • Electrical power is P = VI (equivalently I²R or V²/R), the rate energy converts from electrical form to heat, light, or motion.
  • Series resistors add directly (R_total = R₁ + R₂ + ...): the same current flows through each, while voltage splits between them.
  • Parallel resistors combine reciprocally (1/R_total = 1/R₁ + 1/R₂ + ...): each branch feels the full voltage, while current splits between paths.