Creating Models

What Creating Models covers

Creating Models is examined in all three written papers — the specification states that Components 01, 02 and 03 each assess content from across all the teaching modules, so nothing is confined to one paper. It covers capacitance and charge storage, energy stored on a capacitor, capacitor discharge and the exponential model, the time constant of an RC circuit, charging a capacitor, investigating capacitor charge and discharge, radioactive decay as a random process, activity, decay constant and half-life, Determining the half-life of an isotope, iterative numerical models of exponential change, exponential curves on linear and logarithmic scales, simple harmonic motion: the defining relationship, solutions and graphs of simple harmonic motion, modelling oscillations step by step, energy in simple harmonic motion, period of a mass–spring system and a simple pendulum and free and forced vibrations, damping and resonance.

The 17 subtopics

Each one has its own page.

• Capacitance and charge storageRecall questions on the defining equation and its unit, why practical values are small, charge–voltage calculations and graphs, current as charge arriving, and why the net charge is zero.Open →
• Energy stored on a capacitorRecall questions on why the stored energy is not simply charge times voltage, the equivalent expressions, area under a charge–voltage graph, delivering large power briefly, and where a battery's energy goes.Open →
• Capacitor discharge and the exponential modelRecall questions on why capacitor discharge is exponential, dQ/dt = −Q/(RC) and its minus sign, the constant-ratio property and testing for it, Q = Q₀exp(−t/RC), potential difference and current I = I₀exp(−t/RC) during discharge, the shape of the discharge curve, successive halvings, the effect of resistance, and the initial current.Open →
• The time constant of an RC circuitRecall questions on the time constant τ = RC and its unit, the 37% left after one time constant, calculating τ, the half-life t½ = τ ln 2, treating a capacitor as discharged after five time constants, finding τ from a graph or the initial tangent, the potential difference after a given time, changing R and C, and why larger capacitance slows discharge.Open →
• Charging a capacitorRecall questions on Q = Q₀(1 − exp(−t/RC)) and V = V₀(1 − exp(−t/RC)), the 63% stored after one time constant, why the charging current falls and I = I₀exp(−t/RC), current–time graphs for charging and discharging, time constant and potential difference calculations, the resistor and capacitor potential differences, series resistance, and stored energy.Open →
• Investigating capacitor charge and dischargeRecall questions on the circuit used, what is recorded against time, choosing components so a run can be hand-timed, the time constant from a logarithmic plot, and confirming exponential decay.Open →
• Radioactive decay as a random processRecall questions on the random and spontaneous nature of radioactive decay, why the decay rate is proportional to the nuclei remaining, dN/dt = −λN and the decay constant, fluctuating count rates, demonstrating randomness, why the exponential model works, subtracting background, comparing capacitor discharge with decay, heating a source, and samples of different size.Open →
• Activity, decay constant and half-lifeRecall questions on activity and A = λN, half-life and T½ = ln 2 / λ, N = N₀exp(−λt), calculating half-lives, decay constants and activities from data, activity after several half-lives, ln A against time graphs and their gradient, and why long-lived sources stay hazardous.Open →
• Determining the half-life of an isotopeRecall questions on the protactinium generator method, correcting for background, reading a half-life from a decay curve or a logarithmic plot, keeping the geometry fixed, counting statistics, and handling precautions.Open →
• Iterative numerical models of exponential changeRecall questions on step-by-step solutions of dQ/dt = −Q/(RC) and radioactive decay, calculating single steps, why such models predict too fast a fall, improving accuracy with smaller steps and the drawback of doing so, choosing a step size, checking against N = N₀exp(−λt) and in a spreadsheet, the graphical tangent method, and negative outputs.Open →
• Exponential curves on linear and logarithmic scalesRecall questions on exponential decay on linear and logarithmic axes, why logarithms give a straight line, the intercept of ln V and gradient of ln N against time, spotting background counts, linearising capacitor charging, the constant-ratio property, why decay never reaches zero, gradient as current, finding the time constant, successive halvings, and logarithmic scales.Open →
• Simple harmonic motion: the defining relationshipRecall questions on defining simple harmonic motion, a = −ω²x and its minus sign, the restoring force condition, the mass–spring equation of motion and ω = √(k/m), ω = 2πf, amplitude and period, calculating angular frequency, maximum acceleration and maximum speed, zero acceleration at equilibrium, and why the period is independent of amplitude.Open →
• Solutions and graphs of simple harmonic motionRecall questions on the sine and cosine solutions of simple harmonic motion and when each applies, writing them with frequency, the displacement–time graph, the phase of velocity and acceleration against displacement, gradients linking the graphs, greatest speed at equilibrium, amplitude, angular frequency and maximum speed from x = 0.020 sin(30t), and spotting traces that are not simple harmonic.Open →
• Modelling oscillations step by stepRecall questions on setting up the calculation for a mass on a spring, the starting conditions needed, recalculating acceleration each step, errors from too large a step, energy checks, and damping.Open →
• Energy in simple harmonic motionRecall questions on energy stored ½kx² and Hooke's law F = kx, total energy ½mv² + ½kx², how kinetic and potential energy interchange, where kinetic energy is zero or greatest, calculating stored and total energy, maximum speed and kinetic energy at a displacement, energy in proportion to amplitude squared, and energy–displacement and energy–time graphs.Open →
• Period of a mass–spring system and a simple pendulumRecall questions on the two period equations and frequency, calculations for given masses, stiffnesses and lengths, why the bob's mass does not matter, timing from equilibrium, and squared-period graphs.Open →
• Free and forced vibrations, damping and resonanceRecall questions on free and forced vibrations, natural frequency, damping, lightly damped, critically damped and overdamped motion, resonance and resonance curves, how damping changes the peak, the phase at resonance, observing resonance with a mass on a spring and Barton's pendulums, useful and harmful resonance, and damped car suspension.Open →

What you need to know

Answer each one before you reveal it.

Take Creating Models further

The same content, four other ways.

Commonly confused

Pairs that lose marks when they are blurred together.

• Time constant τ vs Half-life of a discharge

  Time constant τ: the product RC, this being the interval in which the charge left on the capacitor falls to 37%, since e⁻¹ = 0.37. Half-life of a discharge: The interval in which the charge left on the capacitor falls to 50%, equal to RC ln 2, which is about 0.69RC.

• Activity vs Count rate

  Activity: the number of nuclei that decay each second in the whole source, measured in becquerels. Count rate: The number of decays the detector actually registers each second, only a fraction of those in the source and swollen by background radiation.

• Angular frequency ω vs Frequency f

  Angular frequency ω: the rate of oscillation expressed in rad s⁻¹, equal to 2π multiplied by the number of complete cycles each second. Frequency f: The number of complete cycles each second, measured in hertz.

Questions from this topic

Each one with the model answer underneath.

1. 1

   What does the capacitance of a capacitor tell you?

   Model answer

   It is the charge stored per unit potential difference across it, so it measures how much charge the capacitor holds for each volt applied.

2. 2

   What equation defines capacitance?

   Model answer

   Capacitance is C = Q/V, where Q is the charge on either plate and V is the potential difference across the capacitor.

3. 3

   Define the farad.

   Model answer

   One farad is the capacitance of a capacitor that stores one coulomb of charge for each volt of potential difference across it, so 1 F = 1 C V⁻¹.

4. 4

   Why are practical capacitor values usually quoted in microfarads or picofarads?

   Model answer

   The farad is a very large unit, so everyday capacitors have capacitances of the order of 10⁻⁶ F or 10⁻¹² F.

5. 5

   A capacitor holds 4.4 × 10⁻³ C when the potential difference across it is 20 V. What is its capacitance?

   Model answer

   C = Q/V = 4.4 × 10⁻³ / 20 = 2.2 × 10⁻⁴ F, which is 220 μF.

6. 6

   A 470 μF capacitor is charged to 9.0 V. How much charge does it store?

   Model answer

   Q = CV = 470 × 10⁻⁶ × 9.0 = 4.2 × 10⁻³ C.

What is inside Levo

Six ways to work the same material.

Creating Models revision questions

What does Creating Models cover in OCR A-Level Physics B?

17 subtopics: capacitance and charge storage, energy stored on a capacitor, capacitor discharge and the exponential model, the time constant of an rc circuit, charging a capacitor, investigating capacitor charge and discharge, radioactive decay as a random process, activity, decay constant and half-life, determining the half-life of an isotope, iterative numerical models of exponential change, exponential curves on linear and logarithmic scales, simple harmonic motion: the defining relationship, solutions and graphs of simple harmonic motion, modelling oscillations step by step, energy in simple harmonic motion, period of a mass–spring system and a simple pendulum and free and forced vibrations, damping and resonance. Each one has its own page with questions and model answers.

How is Creating Models organised?

By the OCR H557 specification, subtopic by subtopic, so it matches the order you are taught it in.