Physics 1B: Circuits & Ohm's Law

Current — charge in motion

An electric current is the rate at which charge flows past a point in a circuit. Formally:

I = ΔQ / Δt

Where I is current in amperes (A), ΔQ is charge that passed in coulombs (C), and Δt is the time interval in seconds. One ampere equals one coulomb per second — a substantial current. A typical incandescent light bulb draws about 0.5 A; a laptop charger might draw 2 A.

An important convention: conventional current is defined as the flow of positive charge (from + to − through the external circuit). In actual metal wires, electrons (negatively charged) are what physically move — from − toward +. Every result in this course works out correctly using either convention, but the CBE and every diagram you will encounter uses conventional current. When the problem says "current flows this way," it means positive-current direction.

Voltage — the driver

Voltage, also called potential difference, is the electrical "pressure" that drives current through a circuit. It measures energy per unit charge:

V = Energy / Charge         unit: volt (V) = joule/coulomb (J/C)

A 9-volt battery does 9 joules of work on every coulomb of charge that passes through it. A wall outlet at 120 volts does 120 joules of work per coulomb. High voltage is why transmission lines can carry the same power over long distances with lower current (and lower resistive losses).

Think of a circuit like a plumbing system: voltage is the pressure difference between two points, current is the flow of water, and resistance is a narrow section that fights the flow. Understanding this analogy will keep you oriented through every circuit problem.

Resistance and Ohm's law

Resistance is how much a component opposes the flow of current when a voltage is applied. The unit is the ohm (Ω, capital omega). A typical wire in a lab experiment might have negligible resistance; a resistor deliberately designed to control current might range from a few ohms to millions of ohms.

For many conductors — those that obey Ohm's law — voltage, current, and resistance are simply related:

V = I · R

Or in rearranged forms: I = V/R, R = V/I. Ohm's law is a linear relationship: doubling the voltage across a resistor doubles the current through it. Many real components (semiconductors, filaments in old lightbulbs) do NOT obey Ohm's law exactly, but every problem you will see on the Physics 1B CBE assumes ohmic behavior.

Power in circuits

The power dissipated by a circuit element — the rate at which it converts electrical energy to heat, light, or work — is:

P = I · V

Unit: watt (W) = joule/second. With Ohm's law you can rewrite this in three useful forms:

• P = IV — use when you know current and voltage.
• P = I²R — use when you know current and resistance. (Substitute V = IR into IV.)
• P = V²/R — use when you know voltage and resistance. (Substitute I = V/R.)

All three give the same answer for the same problem. Pick the form that uses the two quantities you actually have.

Resistors in series

In a series circuit, resistors are connected end-to-end so the same current flows through each. The current has only one path to take.

Key facts for series circuits:

• Total resistance: R_total = R₁ + R₂ + R₃ + … (simply add them up)
• Current is the same through all resistors: I₁ = I₂ = I₃ = I.
• Voltages add: V_total = V₁ + V₂ + V₃, and each V_n = I·R_n. Larger resistors "drop" more voltage.

Practical consequence: adding more resistors in series reduces the current through the circuit (higher total resistance). Christmas tree lights of the old wired-in-series style all go dark if one bulb burns out — because a burned bulb creates infinite resistance, breaking the single path.

Resistors in parallel

In a parallel circuit, resistors are connected across the same two points so the same voltage is applied to each. Current has multiple paths to choose from.

Key facts for parallel circuits:

• Total resistance: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + … Total resistance is always LESS than the smallest single resistance.
• Voltage is the same across all branches: V₁ = V₂ = V₃ = V.
• Currents add: I_total = I₁ + I₂ + I₃, and each I_n = V/R_n. Smaller resistors carry more current.

Practical consequence: adding more parallel branches DECREASES total resistance, so total current increases. If one bulb in a parallel-wired lamp burns out, the others keep working — they each have their own path.

Where students lose points

• Applying series rules to parallel circuits. Total resistance in parallel is NOT the sum. Use the reciprocal formula.
• Assuming current is the same everywhere. In series it is. In parallel it splits. Always identify which arrangement you have first.
• Forgetting units. Volts, amps, ohms, watts — each has a specific meaning and unit. Do not mix them up.
• Mixing up P = IV, P = I²R, P = V²/R. They are equivalent but use different variables. Choose the form matching what you know.

Worked example — three resistors, mixed configuration

Two resistors of 6 Ω each are connected in parallel. That combination is connected in series with a third 4 Ω resistor. A 10 V battery drives the circuit. Find the total resistance, the current from the battery, and the power dissipated by the 4 Ω resistor.

Step 1 — Parallel combination: 1/R_p = 1/6 + 1/6 = 2/6, so R_p = 3 Ω.

Step 2 — Total: R_p in series with 4 Ω = 3 + 4 = 7 Ω.

Step 3 — Current from battery: I = V/R_total = 10/7 ≈ 1.43 A.

Step 4 — Power in the 4 Ω resistor: P = I²R = (1.43)² × 4 ≈ 8.16 W.

Check yourself

1. Define current, voltage, and resistance in one sentence each.
2. State Ohm's law and rewrite it in three algebraic forms.
3. Give the three equivalent formulas for electrical power.
4. State the total-resistance formulas for series and parallel circuits.
5. Explain why total resistance in parallel is always less than any single resistance in the group.
6. A 12 V battery is connected to a 6 Ω resistor. Find the current and the power dissipated.

(Answer to #6: I = 12/6 = 2 A. P = IV = 2 × 12 = 24 W. Also P = I²R = 4 × 6 = 24 W or P = V²/R = 144/6 = 24 W — all three agree.)

Practice with CBE-style questions

Circuit analysis is a core topic on the Physics Semester B CBE and appears in nearly every practice bank filter. Work through the practice bank filtered by Circuits & Ohm's Law — every question includes a step-by-step solution.

Independent practice content aligned to Texas Essential Knowledge and Skills (TEKS) §112.39(c)(5)(F). Not affiliated with TTU K-12, UT High School, UT-Austin, the Texas Education Agency, or any Credit by Examination administrator. Texas CBE™ does not administer any exam or grant academic credit.