Chapter distribution vs. your proficiency map
| Chapter | # Questions | Your Strength |
|---|---|---|
| Electric Charges & Fields | 3 | Low |
| Moving Charges & Magnetism | 3 | Low |
| Alternating Current | 3 | Low |
| Wave Optics | 3 | Low |
| Nuclei | 2 | Low |
| Electrostatic Potential & Capacitance | 3 | Medium |
| Magnetism & Matter | 2 | Medium |
| Electromagnetic Waves | 2 | Medium |
| Dual Nature of Radiation & Matter | 2 | Medium |
| Semiconductor Electronics | 3 | Medium |
| Current Electricity | 4 | High |
| Electromagnetic Induction | 3 | High |
| Ray Optics & Optical Instruments | 3 | High |
| Atoms | 2 | High |
Goal: see how the paper maps to your syllabus strengths.
Class XII Physics – Electric Charges & Fields
A non-conducting spherical shell of radius \(R\) carries surface charge density \(\sigma(\theta)=\sigma_0\cos\theta\). Using Gauss’s law, find the electric field (magnitude & direction) (i) inside the shell \((r<R)\) and (ii) outside the shell \((r>R)\).
Spherical shell with \(\sigma=\sigma_0\cos\theta\)
Choose a spherical Gaussian surface of radius \(r\) concentric with the shell.
Evaluate \(Q_{\text{encl}}=\int \sigma_0\cos\theta\,dA\) using \(dA=R^2\sin\theta\,d\theta\,d\phi\).
The integral is zero for any \(r\). Hence flux is zero, so \(E=0\) inside. Outside, treat the shell as a dipole with moment \(p=\frac{4\pi R^{3}\sigma_0}{3}\) and use the standard dipole field.
Find enclosed charge first; then relate \( \Phi_E \) to \(E\).
Compare with a uniformly charged shell and with a point dipole.
Sketch positive and negative hemispheres to see the dipole pattern.
Replace \(\cos\theta\) with a constant to check your method gives Coulomb’s law.
Struggle is normal! Try to solve on your own before checking the hints.
CBSE Class 12 • Physics
A proton enters a uniform 0.20 T magnetic field with speed \(2\times10^{6}\,\text{m s}^{-1}\) at \(60^{\circ}\) to the field. Find (a) the radius of its circular path and (b) the pitch of the helix it traces.
Resolve the velocity into \(v_{\perp}\) and \(v_{\parallel}\) using sine and cosine of \(60^{\circ}\).
The Lorentz force bends only \(v_{\perp}\). Use \( r=\frac{m v_{\perp}}{qB} \) for the circle.
Calculate \( T=\frac{2\pi m}{qB} \). Then pitch = \( v_{\parallel} T \). Take \( m_p=1.67\times10^{-27}\,\text{kg} \), \( q_p=1.6\times10^{-19}\,\text{C} \).
Treat perpendicular and parallel motions separately.
Recall \(r=mv/qB\) from uniform circular motion in a magnetic field.
Draw the helical path around straight field lines.
Imagine \(60^{\circ}=90^{\circ}\) to check understanding of pure circular motion.
Struggle is normal! Try to solve on your own before checking the hints.
Class 12 Physics – Alternating Current
An ideal series L-C-R circuit has L = 50 mH, C = 80 µF, R = 40 Ω and is driven by a 200 V, 50 Hz source. Find (a) the current amplitude and (b) the phase angle between current and source voltage.
Start by comparing \(X_L\) and \(X_C\) at 50 Hz. Which one is larger?
Numeric check: \(X_L \approx 15.7 Ω\), \(X_C \approx 39.8 Ω\). The circuit is capacitive.
Compute \(Z\) with the above values, use \(I_0 = V_0 / Z\). Find \(\tan\phi\); negative sign means current leads the voltage.
Treat reactances, resistance and voltage separately before combining.
Recall DC Ohm’s law—impedance plays the same role in AC.
Sketch the impedance triangle to see how \(R\) and \((X_L-X_C)\) combine.
Set C very large; notice how the circuit approaches a pure inductor–resistor pair.
Struggle is normal! Try to solve on your own before checking the hints.
Wave Optics – CBSE Class 12
In a YDS set-up (λ = 600 nm, d = 0.5 mm, D = 1.5 m) a mica sheet (μ = 1.5) covers one slit so the central maximum shifts to the 3rd bright fringe. Find the sheet thickness t.
Which path difference makes the central bright coincide with the 3rd bright?
Compute \( \Delta = 3\lambda \) and link it to the sheet by \( (\mu - 1)t \).
Set \( (\mu - 1)t = 3\lambda \). With \( \lambda = 600\,\text{nm} \) and \( \mu = 1.5 \), you will get \( t = 3.6\,\mu\text{m} \).
Isolate fringe shift first, then apply sheet optics.
Recall how glass slabs create phase difference in interference.
Sketch fringe pattern before and after inserting mica.
Solve for \( m = 1 \) to check your method, then scale.
Struggle is normal! Try to solve on your own before checking the hints.
Nuclei – Fusion
Two deuterons fuse: \(^{2}\text{H}+^{2}\text{H}\rightarrow{}^{3}\text{He}+n\). Given \(BE(^{2}\text{H}) = 1.113\ \text{MeV}\) and \(BE(^{3}\text{He}) = 7.718\ \text{MeV}\), compute the released energy \(Q\).
Add the binding energies of both reactant deuterons first.
The neutron is free, so its binding energy is zero; only \(^{3}\text{He}\) contributes for products.
Use \(Q = BE_{\text{products}} - BE_{\text{reactants}}\). A positive \(Q\) means energy is released.
Compute reactant and product totals separately, then compare.
Recall \(E=\Delta m c^{2}\): mass defect converts directly to energy.
Sketch energy levels; the deeper (more negative) level is more stable.
Try fusing one deuteron with a neutron to verify your calculation steps.
Struggle is normal! Try to solve on your own before checking the hints.
Electrostatic Potential & Capacitance
Three identical parallel-plate capacitors, each of capacitance \(C\), are connected in series to a 300 V source. While the circuit is live, the middle capacitor is completely filled with a dielectric of constant \(\kappa = 4\). Determine (i) the charge on every capacitor and (ii) the total energy stored in the combination.
Treat the middle capacitor as \(C' = 4C\) once the dielectric is inserted.
Find \(C_{\text{eq}}\) of the series set, then compute common charge \(Q = C_{\text{eq}} \times 300\text{ V}\).
Voltage drops: \(V_1 = Q/C\), \(V_2 = Q/C'\), \(V_3 = Q/C\). Check they sum to 300 V, then add energies: \(U = \tfrac12 \sum C_i V_i^2\).
Analyze each capacitor, then combine their effects.
Remember: charge is identical across capacitors in series.
Draw potential drops across the three plates.
Set \(\kappa = 1\) first; compare the result to see the dielectric’s impact.
Struggle is normal! Try to solve on your own before checking the hints.
CBSE Class 12 Physics
A bar magnet oscillates freely in Earth’s horizontal field \(B_H = 3.6 \times 10^{-5}\,\text{T}\). Its time period is \(2\,\text{s}\).
(a) Find its magnetic moment \(M\).
(b) How far from the centre on the axial line will the net field be zero?
Diagram (if needed)
Start with the oscillation relation linking \(T\), \(I\), \(M\) and \(B_H\).
Rearranged: \(M = \frac{4\pi^2 I}{B_H T^2}\). For a slender rod, \(I \approx m\ell^2/12\).
For part (b) set the dipole’s axial field opposite to Earth’s: \(\frac{\mu_0}{4\pi}\frac{2M}{r^3}=B_H\). Solve for \(r\).
Tackle part (a) to get \(M\); use it immediately in part (b).
Remember tangent law uses the same \(M/B_H\) ratio—consistent ideas help.
Sketch field lines; mark where the magnet’s axial field cancels Earth’s.
Assume \(M = 1\,\text{A·m}^2\) to verify your algebra before inserting numbers.
Struggle is normal! Try to solve on your own before checking the hints.
Physics – Class XII
An EM wave with peak electric field \(E_0 = 6\;\text{V\,m}^{-1}\) travels along +x. (i) Write expressions for \(\mathbf{E}(x,t)\) and \(\mathbf{B}(x,t)\). (ii) Find (a) the magnetic field amplitude and (b) the average energy flux.
Start with \(B_0 = E_0/c\) from Maxwell’s equations.
Choose \(\mathbf{E}\parallel\hat{j}\), \(\mathbf{B}\parallel\hat{k}\) so both are ⟂ to +x.
Write sine wave forms, compute \(B_0\), then use \(S_{\text{avg}} = E_0B_0/(2\mu_0)\).
Treat amplitude, orientation, and energy flux as separate mini-tasks.
Recall that \(c = 3\times10^{8}\,\text{m s}^{-1}\) links E and B fields.
Sketch mutually perpendicular \(\mathbf{E}\), \(\mathbf{B}\) and propagation axes.
Check with \(E_0=1\;\text{V m}^{-1}\) to avoid confusion between rms and peak values.
Struggle is normal! Try to solve on your own before checking the hints.
Dual Nature of Radiation & Matter
Light of wavelength 248 nm falls on a metal with work function 2 eV.
(a) Calculate the maximum kinetic energy of the emitted electrons.
(b) What accelerating potential must be applied so their de Broglie wavelength becomes 0.50 Å?
First find photon energy from its wavelength, then subtract the work function.
Convert \(E_{\gamma}=\frac{hc}{\lambda}\) to eV. Use \(K_{\max}=E_{\gamma}-2\text{ eV}\). For part (b), add \(eV_{\text{acc}}\) to \(K_{\max}\) before using the de Broglie formula.
Step 1: Compute \(K_{\max}\).
Step 2: Set \( \lambda =0.50\; \text{Å}=5.0\times10^{-11}\,\text{m}\).
Step 3: Solve \( \lambda =\frac{h}{\sqrt{2m(K_{\max}+eV_{\text{acc}})}} \) for \(V_{\text{acc}}\).
Tackle part (a) completely before using its result for part (b).
Recall how work function limits electron energy in photoelectric effect.
Sketch an energy bar showing photon energy, work function, \(K_{\max}\), and extra energy from acceleration.
Try λ = 1 Å first to see how potential affects wavelength before calculating the exact value.
Struggle is normal! Try to solve on your own before checking the hints.
Semiconductor Electronics – CE Amplifier
For a silicon npn transistor in common-emitter mode, \(R_C = 2\,\text{k}\Omega\), \(R_E = 1\,\text{k}\Omega\) and \(\beta = 120\). A \(1\,\text{mV rms}\) input is fed through a \(1\,\text{k}\Omega\) base resistor.
(a) Find the small-signal voltage gain \(A_v\).
(b) Discuss the bias stability of this amplifier.
No additional diagram required
Calculate \(I_b = \frac{1\,\text{mV}}{1\,\text{k}\Omega}\) and then find \(I_C = \beta I_b\).
Use \(r_e = 25\,\text{mV}/I_C\); expect \(r_e\) to be a few hundred ohms.
Insert \(r_e\) into \(A_v\). Note \((\beta + 1)R_E\) dominates the denominator, so \(A_v \approx -2\). Large \(R_E\) lowers gain but locks \(I_C\), giving excellent bias stability.
Separate dc bias calculation from ac gain evaluation.
Recall that emitter degeneration reduces gain but improves stability.
Sketch the small-signal model to see resistances in the signal path.
Ignore \(R_E\) briefly to observe how gain would rise to \(-\beta R_C/r_e\).
Struggle is normal! Try to solve on your own before checking the hints.
CBSE Class 12 Physics – Current Electricity
A uniform wire of resistance \(2\,\Omega\) is bent into a square. Determine the resistance between opposite corners. The wire is then stretched so one side becomes twice its original length, volume constant. Find the new resistance between the same opposite corners.
Sketch the square and label resistances.
First, compute resistance between corners when each side is \(0.5\,\Omega\).
Treat the square as a balanced Wheatstone bridge; ignore the diagonal branch.
Stretching doubles one side’s length. Remaining three sides shorten equally. Use \(R \propto l^2\) then re-apply the bridge reduction.
Analyse pre-stretch and post-stretch networks separately.
Recall meter-bridge balance ⇒ equal potential nodes cancel internal branch.
Sketch potentials on the square; mark equipotential corners.
Imagine stretching until three sides vanish; check if trend matches answer.
Struggle is normal! Try to solve on your own before checking the hints.
Class XII Physics – Electromagnetic Induction
A circular coil of 200 turns and area 0.02 m² rotates at 300 rpm about its diameter in a uniform 0.04 T field. (a) Derive the expression for the instantaneous induced emf. (b) Calculate the peak emf produced.
Visualise the rotating coil of an AC generator.
Start by writing the magnetic flux through one turn as a time-dependent cosine.
Differentiate \( \Phi \) with respect to \( t \) to get \( \varepsilon \); then multiply by 200 turns.
Convert 300 rpm to \( \omega = 2\pi n \). Use \( \varepsilon_{0}=N B A \omega \) to find \( \approx 5.0\; \text{V} \).
First derive the formula, then plug numbers.
Recall how generators convert rotation to alternating voltage.
Sketch coil positions for \( \cos \) and \( \sin \) angles.
Analyze a single-turn loop, then scale by 200.
Struggle is normal! Try to solve on your own before checking the hints.
Ray Optics & Optical Instruments
A refracting telescope has an objective of focal length 80 cm and an eyepiece of focal length 4 cm. The final image is at infinity.
(a) Find the lens separation.
(b) Determine the angular magnification.
(c) What objective diameter gives 200× the light-gathering power of a 6 mm pupil?
In normal adjustment, the objective image lies at the eyepiece focal plane.
Use \(d = f_0 + f_e\) for separation and \(M = f_0 / f_e\) for magnification.
Calculate \(M = 80/4\). For light power, set \(\left(\frac{D_0}{6\text{ mm}}\right)^2 = 200\) and solve for \(D_0\).
Solve parts (a), (b), and (c) one after another.
Link magnification to focal-length ratios you learned for simple lenses.
Draw a ray diagram of the telescope in normal adjustment.
Try equal focal lengths to check if your formulas give \(M = 1\).
Struggle is normal! Try to solve on your own before checking the hints.
Atoms • Hydrogen Spectrum
Using Bohr postulates, derive the wavelength expression for the Balmer series (transitions to \(n_1 = 2\)) and calculate its shortest-wavelength limit.
Write \( \Delta E = 13.6\,\text{eV}\,(1/n_1^2 - 1/n_2^2) \) for the photon released.
Substitute \(n_1 = 2\). Use \( \Delta E = hc/\lambda \) to obtain \(1/\lambda\).
Let \(n_2 \to \infty\). Then \(1/\lambda_{\min} = R/4\), so \( \lambda_{\min} \approx 364.6\,\text{nm} \).
Identify initial and final levels, compute \( \Delta E \), then convert to \( \lambda \).
Remember Balmer lines lie in the visible region; check if your answer fits.
Sketch energy levels and draw arrows for transitions to \( n=2 \).
Calculate \( \lambda \) for \( n_2 = 3 \) first to verify your method.
Struggle is normal! Try to solve on your own before checking the hints.
Quick recap—verify symmetry, then apply \( \oint \vec{E}\!\cdot\!d\vec{A}=q_{\text{enc}}/\varepsilon_0 \).
Resolve \( \vec{v} \) into parts ⟂ and ∥ \( \vec{B} \) for instant path insight.
Judge lead/lag and impedance size before any AC number-crunching.
Use \( \Delta = d\sin\theta \) to locate fringes swiftly in interference.
Compute mass or binding-energy change, then apply \(E=\Delta m c^{2}\).
Add emitter resistance in BJT small-signal diagrams for accurate gain.
Last-minute things to remember: write rad, J, T clearly to avoid slips.