FAD1022: BASIC PHYSICS II — Interleaved Mastery Problem Set

4-Day Intensive Study Plan
Topics: Electrostatics, Capacitors, AC Circuits, Magnetism, Inductance, Semiconductors, Modern Physics

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How to Use This Set

Each problem weaves together 2-4 physics topics in realistic technological and natural contexts. This trains the pattern-recognition essential for solving exam problems where the approach isn't given.

Study Schedule:

• Day 1: Problems 1-3 (Electronics & Power Systems)
• Day 2: Problems 4-6 (Medical & Quantum Applications)
• Day 3: Problems 7-9 (Energy & Materials)
• Day 4: Problems 10-12 (Synthesis & Design)

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Physics Topics Concept Map

graph TD
    A[Physics II Problems] --> B[Electrostatics]
    A --> C[AC Circuits]
    A --> D[Magnetism & Inductance]
    A --> E[Modern Physics]
    A --> F[Semiconductors]
    B --> B1[Coulombs Law]
    B --> B2[Capacitors]
    B --> B3[Electric Fields]
    C --> C1[Transformers]
    C --> C2[Power Factor]
    C --> C3[Resonance]
    D --> D1[Solenoids]
    D --> D2[EM Induction]
    D --> D3[Mutual Inductance]
    E --> E1[Photoelectric Effect]
    E --> E2[Bohr Model]
    E --> E3[Nuclear Physics]
    F --> F1[Diodes]
    F --> F2[Band Gap Energy]
    B2 --> G[Problem 1: Touchscreen]
    C1 --> H[Problem 3: Power Grid]
    D1 --> I[Problem 2: MRI]
    E1 --> J[Problem 5: Smoke Detector]
    F1 --> K[Problem 4: Rectifier]
    D3 --> L[Problem 7: Wireless Charging]
    D2 --> M[Problem 8: Hall Sensor]
    E2 --> N[Problem 9: Spectroscopy]
    C3 --> O[Problem 7: Resonance]

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The Mastery Problems

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Problem 1: Smartphone Touchscreen [Electrostatics + Capacitors + Energy]

A capacitive touchscreen uses a grid of capacitors. A finger touch changes capacitance by effectively adding a parallel plate.

Given: Original capacitor $C_0 = 2.0$ pF, plate area $A = 4.0$ mm², dielectric constant $\kappa = 3.5$ (glass), finger adds $\Delta C = 0.5$ pF, operating voltage $V = 3.3$ V.

(a) Calculate the original plate separation and the electric field strength in the glass. [Capacitors]

(b) When touched, the capacitance increases. Calculate the new capacitance and the change in stored energy. Where does this energy go? [Capacitor energy]

(c) The finger acts as a conductor at body potential. Model the finger as a conducting sphere of radius 1.0 cm at potential $V_{body}$. Calculate the charge induced on the finger if $V_{body} = 0.1$ V relative to ground. [Electrostatics]

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Problem 2: MRI Machine Magnet [Magnetism + Inductance + Energy]

An MRI solenoid has $N = 1000$ turns, length $l = 2.0$ m, radius $r = 0.5$ m, carrying $I = 100$ A to produce $B = 1.5$ T.

(a) Verify the magnetic field using $B = \mu_0 n I$ and calculate the inductance of the solenoid. [Magnetism + Inductance]

(b) The magnet is ramped up from 0 to 100 A in 60 seconds. Calculate the back EMF during ramp-up and the total energy stored in the magnetic field at full current. [Inductance + Energy]

(c) The field must be uniform within 0.1%. Calculate the maximum variation in $B$ allowed and the corresponding tolerance in current. [Error analysis]

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Problem 3: Power Grid Transformer [AC Circuits + Transformers + Power]

A step-down transformer delivers 240 V to homes from 11 kV lines. The secondary supplies 100 A to a residential load with power factor 0.85 lagging.

(a) Calculate the turns ratio and the primary current (assuming ideal transformer). [Transformers]

(b) The load consists of resistive heating (pf = 1) and an induction motor (pf = 0.75). Calculate the reactive power and the apparent power drawn from the grid. [AC Power]

(c) A capacitor bank is added to improve pf to 0.95. Calculate the required capacitance and the new current drawn from the grid. [Power factor correction]

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Problem 4: Semiconductor Device [Semiconductors + AC Analysis + Energy Bands]

A silicon diode has $n_i = 1.5 \times 10^{10}$ cm⁻³ at 300 K, band gap $E_g = 1.1$ eV, and is doped with $N_D = 10^{16}$ cm⁻³ donors.

(a) Calculate the electron and hole concentrations in the n-type region at 300 K and 400 K. [Semiconductor physics]

(b) The diode is used in a half-wave rectifier with $V_{rms} = 12$ V, 50 Hz, load $R = 100$ Ω. Calculate the DC output voltage and the ripple factor. [AC Circuits + Rectification]

(c) For a solar cell application, calculate the maximum open-circuit voltage given the built-in potential and the wavelength of light that can be absorbed. [Photovoltaics]

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Problem 5: Photoelectric Smoke Detector [Modern Physics + Circuits + Energy]

A smoke detector uses americium-241 ($E_{\gamma} = 59.5$ keV) to ionize air. The photoelectric effect in the ionization chamber creates a current.

(a) Calculate the maximum kinetic energy of photoelectrons ejected from a gold cathode (work function $\phi = 5.1$ eV). Calculate the cutoff frequency. [Photoelectric effect]

(b) The chamber has capacitance $C = 10$ pF and resistance $R = 10^{10}$ Ω. Calculate the RC time constant and the voltage decay when smoke reduces the ionization current by 50%. [RC Circuits]

(c) Calculate the number of photons per second needed to maintain a steady current of 1.0 nA, and the corresponding power of the Am-241 source. [Modern Physics + Circuits]

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Problem 6: Particle Accelerator [Magnetism + Electrostatics + Modern Physics]

A cyclotron accelerates protons using a magnetic field $B = 1.0$ T and alternating voltage $V_{max} = 50$ kV between dees of radius $R = 0.5$ m.

(a) Calculate the cyclotron frequency and the maximum kinetic energy of the protons. [Magnetism - Lorentz force]

(b) Derive the number of orbits needed to reach maximum energy and the total time for acceleration. [Modern Physics + Mechanics]

(c) If the protons are used to bombard a lithium target, calculate the threshold energy for the reaction $^7\text{Li} + p \rightarrow 2\alpha$ given masses: $m_{^7\text{Li}} = 7.016$ u, $m_p = 1.008$ u, $m_{\alpha} = 4.003$ u. [Nuclear Physics]

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Problem 7: Wireless Charging Pad [AC Circuits + Inductance + Electromagnetic Induction]

A Qi wireless charger uses two coupled inductors: transmitter $L_1 = 10$ μH, receiver $L_2 = 5.0$ μH, coupling coefficient $k = 0.6$, operating at $f = 100$ kHz.

(a) Calculate the mutual inductance and the equivalent inductance seen by the source. [Mutual inductance]

(b) The receiver has a load $R = 5.0$ Ω. Calculate the reflected impedance to the primary and the power transfer efficiency. [AC Circuits + Transformers]

(c) Calculate the resonant capacitance needed for both coils and the maximum power transfer at resonance. [AC Resonance]

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Problem 8: Hall Effect Sensor [Magnetism + Electrostatics + Semiconductors]

A Hall sensor uses an n-type semiconductor strip with $n = 10^{21}$ m⁻³ electrons, dimensions $w = 1.0$ mm, $t = 0.1$ mm, carrying $I = 10$ mA in a perpendicular magnetic field $B = 0.1$ T.

(a) Calculate the Hall voltage and determine which edge is at higher potential. [Hall effect]

(b) Calculate the drift velocity of electrons and the electric field due to the Hall effect. Compare this to the electric field driving the current. [Drift velocity]

(c) If the sensor is used to measure current in a wire without breaking the circuit, explain how this works and calculate the sensitivity (V_H per ampere of wire current). [Applications]

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Problem 9: Atomic Spectroscopy [Modern Physics + Electrostatics + Energy Levels]

Hydrogen spectral lines result from electron transitions. The Lyman series is in UV, Balmer in visible.

(a) Calculate the wavelength of the first three lines of the Balmer series and identify their colors. [Bohr model]

(b) In a gas discharge tube at 300 K, calculate the ratio of atoms in $n=2$ to $n=1$ using Boltzmann distribution. [Statistical mechanics]

(c) An external electric field causes Stark effect splitting. Calculate the energy shift for the $n=2$ level in a field $E = 10^5$ V/m. [Perturbation - qualitative]

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Problem 10: Operational Amplifier Circuit [AC Analysis + Semiconductors + Feedback]

An op-amp audio amplifier has $A_{OL} = 10^5$, input impedance $R_{in} = 1$ MΩ, output impedance $R_{out} = 100$ Ω, with feedback resistors $R_1 = 1$ kΩ, $R_2 = 10$ kΩ.

(a) Calculate the closed-loop gain, input impedance, and output impedance. [Op-amp feedback]

(b) At what frequency does the gain drop to unity if the gain-bandwidth product is 1 MHz? Sketch the Bode plot. [AC Analysis + Frequency response]

(c) The op-amp uses a differential pair input stage. Explain how this provides high CMRR and calculate the CMRR if common-mode gain is 0.01. [Semiconductor circuits]

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Problem 11: Lightning Protection System [Electrostatics + Capacitors + Energy]

A lightning rod protects a building by providing a preferred path to ground. A cloud at 500 m has charge $Q = 50$ C, creating potential difference $V = 10^8$ V with ground.

(a) Calculate the capacitance of the cloud-ground system and the energy stored before discharge. [Capacitors]

(b) Model the lightning channel as a plasma conductor with $R = 10$ Ω. Calculate the peak current, duration (if $Q$ discharges in 1 ms), and power dissipated. [RC + Power]

(c) The rapid current change induces voltage in nearby loops (EMP). Calculate the induced EMF in a 1.0 m² loop 100 m from the strike. [Electromagnetic induction]

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Problem 12: Quantum Communication [Modern Physics + AC Circuits + Detection]

Quantum key distribution uses photon polarization. A photon source emits at $\lambda = 850$ nm with intensity corresponding to 0.1 photon per pulse.

(a) Calculate the photon energy and determine if silicon photodetectors (band gap 1.1 eV) can detect these photons. [Photoelectric effect]

(b) The detector has quantum efficiency $\eta = 0.7$ and dark count rate 100 s⁻¹. Calculate the signal-to-noise ratio for 10⁶ pulses/second. [Detection statistics]

(c) An eavesdropper measuring polarization disturbs the quantum state. Calculate the minimum energy required to distinguish between two orthogonal polarization states within the uncertainty principle. [Modern Physics]

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Summary of Topics Combined

Problem	Topics	Context
1	Electrostatics + Capacitors	Smartphone
2	Magnetism + Inductance	MRI
3	AC Circuits + Transformers	Power grid
4	Semiconductors + AC	Diode rectifier
5	Modern Physics + Circuits	Smoke detector
6	Magnetism + Nuclear	Cyclotron
7	Inductance + AC Circuits	Wireless charging
8	Magnetism + Semiconductors	Hall sensor
9	Modern Physics + Electrostatics	Spectroscopy
10	AC Analysis + Semiconductors	Op-amp
11	Electrostatics + Capacitors	Lightning
12	Modern Physics + AC	Quantum communication

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Key Formulas Reference

Electrostatics

• $F = k\frac{q_1q_2}{r^2}$ (Coulomb's law)
• $E = \frac{kQ}{r^2}$, $V = \frac{kQ}{r}$
• $U = k\frac{q_1q_2}{r}$, capacitance $C = \frac{Q}{V}$

Capacitors

• $C = \frac{\kappa\epsilon_0A}{d}$, $U = \frac{1}{2}CV^2 = \frac{Q^2}{2C}$
• RC circuits: $\tau = RC$, charging $q(t) = Q(1-e^{-t/\tau})$

AC Circuits

• $X_C = \frac{1}{\omega C}$, $X_L = \omega L$, $Z = \sqrt{R^2 + (X_L-X_C)^2}$
• $\tan\phi = \frac{X_L-X_C}{R}$, $P = VI\cos\phi$
• Resonance: $\omega_0 = \frac{1}{\sqrt{LC}}$

Magnetism

• $F = qvB\sin\theta$, $F = ILB\sin\theta$
• $B = \frac{\mu_0NI}{l}$ (solenoid), $\Phi = BA$
• $E = -N\frac{d\Phi}{dt}$ (Faraday's law)

Inductance

• $L = \frac{N\Phi}{I}$, $E = -L\frac{dI}{dt}$
• $U = \frac{1}{2}LI^2$, mutual: $M = k\sqrt{L_1L_2}$

Transformers

• $\frac{V_2}{V_1} = \frac{N_2}{N_1} = \frac{I_1}{I_2}$ (ideal)
• Impedance matching: $Z_{in} = \left(\frac{N_1}{N_2}\right)^2Z_L$

Modern Physics

• $E = hf = \frac{hc}{\lambda}$, photoelectric: $KE_{max} = hf - \phi$
• Bohr: $E_n = -\frac{13.6}{n^2}$ eV, $r_n = n^2a_0$
• $E = mc^2$, mass defect $\Delta m = \text{sum of masses} - \text{product mass}$

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Related Resources

• Electrostatics
• Capacitors & Dielectrics
• AC Circuits
• Magnetism
• Inductance & Transformers
• Semiconductors & Diodes
• Modern Physics — Wave-Particle Duality
• Photons
• Photoelectric Effect

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#physics #interleaved-practice #mastery #fad1022