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Physics 2 Unit 3: Electric circuits

Circuits move charge through resistors and capacitors, governed by Ohm's law and Kirchhoff's rules.

Covers: Current and resistance, Ohm's law, resistivity, electric power, series and parallel circuits, Kirchhoff's rules, RC circuits

Study guide

Electric current is the rate of charge flow: I = Δq/Δt, measured in amperes. Conventional current flows from positive to negative, opposite to electron flow. A battery provides an emf, a potential difference that drives current; real batteries have internal resistance, so the terminal voltage is ΔV = ε − Ir. Resistance opposes current. Ohm's law states ΔV = IR for ohmic materials. A resistor's resistance depends on its material and shape: R = ρL/A, so longer, thinner wires have more resistance, and resistance often rises with temperature. Electric power is P = IΔV = I²R = (ΔV)²/R, and energy used is power times time.

In a series circuit, there's one path; current is the same through every resistor, voltages add, and equivalent resistance is Req = R₁ + R₂ + .... If one element breaks, the whole circuit stops. In a parallel circuit, each branch has the same voltage, currents add, and 1/Req = 1/R₁ + 1/R₂ + ...; adding a branch lowers the total resistance and increases the total current. Household circuits are parallel. Ammeters measure current and are placed in series with very low resistance; voltmeters measure voltage and are placed in parallel with very high resistance.

Kirchhoff's junction rule says the current entering a junction equals the current leaving it (conservation of charge). The loop rule says the sum of potential changes around a closed loop is zero (conservation of energy). Capacitors in parallel add (Ceq = C₁ + C₂), while capacitors in series combine as 1/Ceq = 1/C₁ + 1/C₂. In an RC circuit, a charging capacitor's current starts high and decreases as the capacitor fills; once fully charged, it acts like an open circuit and no current flows through its branch. The time constant τ = RC sets how quickly it charges or discharges.

At the moment a switch closes, an uncharged capacitor has zero potential difference across it and acts like a plain wire. As it charges, its voltage rises toward the battery's emf, and the current decays exponentially. After one time constant (τ = RC), a charging capacitor holds about 63% of its final charge. Because terminal voltage is ΔV = ε − Ir, a graph of ΔV against I is a straight line with slope −r and y-intercept ε. In general, rearrange the equation into the form y = mx + b, so that the unknown quantity is the slope or intercept.

A bulb's brightness depends on the power it dissipates (P = I²R = ΔV²/R). In series, the bulb with the larger resistance is brighter. In parallel, where each bulb has the same voltage, the bulb with the smaller resistance is brighter.

Key ideas

• Current is the rate of charge flow.
• Ohm's law: ΔV = IR.
• Series: same current, resistances add.
• Parallel: same voltage, adding branches lowers total resistance.
• Kirchhoff's rules come from conservation of charge and energy.

Formulas and rules

Common mistakes

• Thinking current is used up by resistors; current is the same everywhere in a series loop.
• Placing a voltmeter in series or an ammeter in parallel.

Words to know

Electric current

The rate of flow of charge.

Ampere

The unit of current, one coulomb per second.

Conventional current

Current direction from positive to negative.

emf

The potential difference a battery provides.

Internal resistance

Resistance inside a battery.

Resistance

Opposition to current, in ohms.

Ohm's law

ΔV = IR.

Resistivity

A material's inherent resistance.

Electric power

The rate of energy transfer: P = IΔV.

Series circuit

A circuit with one path for current.

Parallel circuit

A circuit with multiple branches.

Equivalent resistance

The single resistance that replaces a combination.

Ammeter

A device that measures current, placed in series.

Voltmeter

A device that measures voltage, placed in parallel.

Junction rule

Current into a junction equals current out.

Loop rule

Potential changes around a loop add to zero.

RC circuit

A circuit with a resistor and capacitor.

Time constant

τ = RC, the characteristic charging time.

Sample practice questions

15 more questions like these, from level 1 to 5, are in the practice set.