Revise Current and circuits for IB Physics (B.5)

Electric current is the rate at which charge flows past a point. If a charge $\Delta q$ passes in a time $\Delta t$, the current is $I = \Delta q / \Delta t$, measured in amperes (1 A = 1 C s⁻¹). By convention we take current as the direction positive charge would move, even though in a metal it is electrons that drift the other way. Potential difference is the partner idea: it measures energy, not flow. The p.d. across a component is the electrical energy converted to other forms per unit charge passing through it, $V = W/q$, measured in volts (1 V = 1 J C⁻¹).

$I = \frac{\Delta q}{\Delta t}$

Resistance measures how strongly a component opposes current, defined as $R = V/I$ and measured in ohms ($\Omega$). For many conductors at constant temperature the current is proportional to the p.d.: this is Ohm's law, written $V = IR$ with $R$ constant. Resistance also depends on the physical shape and material of a conductor. A longer wire has more resistance and a thicker wire has less, captured by the resistivity relation $R = \rho L / A$, where $\rho$ is the resistivity of the material (unit $\Omega\,$m), $L$ its length and $A$ its cross-sectional area.

$V = IR \qquad\text{and}\qquad R = \frac{\rho L}{A}$

An I–V characteristic is a graph of current against potential difference for a component. Its shape tells you at a glance whether the component obeys Ohm's law. A metal resistor at constant temperature gives a straight line through the origin — its resistance ($V/I$) is constant, so it is ohmic. A filament lamp gives an S-shaped curve that flattens as the voltage rises: heating the filament raises its resistance, so it is non-ohmic. A diode is strongly non-ohmic — it conducts almost nothing until a threshold forward voltage, then the current rises steeply, and it blocks current in the reverse direction. For any point on any of these graphs the resistance is still $V/I$; only for the straight ohmic line is that ratio constant.

In series, components form a single path, so the SAME current flows through each and the source p.d. is shared between them; resistances simply add. In parallel, components connect across the same two points, so each has the SAME p.d. across it and the current splits between the branches; here the reciprocals of the resistances add. Because extra parallel paths make it easier for charge to flow, the combined parallel resistance is always smaller than the smallest single branch — a fact worth using as a check on every parallel calculation.

$\text{Series: } R_{\text{total}} = R_1 + R_2 + \ldots \qquad \text{Parallel: } \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots$

Power is the rate at which electrical energy is transferred. Combining $P = VI$ (energy per charge times charge per second) with Ohm's law gives three equivalent forms. Use whichever version fits the two quantities you already know: $P = VI$ when you have p.d. and current, $P = I^2R$ when you have current and resistance, and $P = V^2/R$ when you have p.d. and resistance. All give power in watts (W).

$P = VI = I^2 R = \frac{V^2}{R}$

A real cell is not a perfect source. It has an internal resistance $r$ in series with an ideal EMF $\varepsilon$. When a current $I$ flows, some energy is dissipated inside the cell, producing 'lost volts' equal to $Ir$. The voltage actually available to the external circuit — the terminal potential difference — is therefore $V_{\text{terminal}} = \varepsilon - Ir$, which is also just the p.d. across the external load. For a single external resistor $R$ the EMF is shared between load and internal resistance, giving $\varepsilon = I(R + r)$.

$\varepsilon = I(R + r) \qquad V_{\text{terminal}} = \varepsilon - Ir = IR$

Kirchhoff's two laws are the bookkeeping rules that let you analyse any circuit, however it is wired. The first law (the junction rule) says the total current flowing into any junction equals the total current flowing out — nothing more than conservation of charge, and the reason series current is constant while parallel current splits. The second law (the loop rule) says that around any closed loop the sum of the EMFs equals the sum of the potential-difference drops — a statement of conservation of energy, since a unit charge returning to its start must have gained exactly as much energy as it lost.

This is the showcase for a calculation topic. In Paper 2 the marks are analytic: each is tied to a specific piece of working — a method mark (M) or an answer mark (A) — and, crucially, the method marks and error-carried-forward (ECF) mean a wrong number early on does not cost you every mark that follows. That protection only exists if your method is written down. Study how each mark below is earned by a specific line.

The habits built here — track the current with Kirchhoff's junction rule, track the energy with the loop rule, and reach for the right form of the power equation — carry straight into the rest of electricity. Potential dividers are just series p.d.-sharing used deliberately; capacitor and RC work reuses charge, current and energy; and electromagnetic induction generates the very EMFs you have learned to handle here. Master the three-step circuit method — combine the resistances, find the current, then work out each p.d. — and the harder circuit questions become variations on a method you already own.