Disclaimer: Easy Education Tips is an independent educational website and is not connected to the Government of Tamil Nadu or the Directorate of Government Examinations. The problems and solutions below were written by us for practice. They are not past exam questions. Always follow the method and sign conventions in your own textbook and teacher's instructions, and check your answers against your school material.
Many students know the formula but still lose marks in physics numericals. The usual reasons are small: a missing unit, a wrong power of ten, or a sign error. In this post you will learn a simple 5-step method and see it used on 8 solved problems. If you also want question practice, you can use our 12th Physics 2nd Mid-Term Important Questions PDF and apply the same method there.
The 5-step method
- Write what is given. List every value with its unit.
- Convert units first. Change cm to m, μC to C, minutes to seconds before you calculate.
- Write the formula. Write it in symbols before putting in numbers. Examiners give marks for the correct formula.
- Substitute and calculate. Do it in clear lines. Keep powers of ten together.
- State the answer with unit and a short check: is the size sensible?
Problem 1: Coulomb's law
Two point charges of 4 μC and 6 μC are 30 cm apart in air. Find the force between them.
Given: q1 = 4 × 10−6 C, q2 = 6 × 10−6 C, r = 0.3 m, k = 9 × 109 N m² C−2
Formula: F = k q1 q2 / r²
Solution: F = (9 × 109 × 4 × 10−6 × 6 × 10−6) / (0.3)² = (9 × 109 × 24 × 10−12) / 0.09 = 0.216 / 0.09 = 2.4 N, repulsive because both charges are positive.
Common mistake: using 30 instead of 0.3 for r. Always convert cm to m, and remember r is squared.
Problem 2: Capacitor charge and energy
A 5 μF capacitor is charged to 12 V. Find the charge stored and the energy stored.
Given: C = 5 × 10−6 F, V = 12 V
Formulas: Q = CV and U = ½CV²
Solution: Q = 5 × 10−6 × 12 = 60 × 10−6 C = 60 μC. U = ½ × 5 × 10−6 × 144 = 360 × 10−6 J = 360 μJ.
Common mistake: forgetting to square V in the energy formula.
Problem 3: Series and parallel resistors
A 6 Ω and a 3 Ω resistor are connected in parallel. This combination is connected in series with a 4 Ω resistor across a 12 V battery. Find the total current and the current through each parallel resistor.
Step 1, parallel part: Rp = (6 × 3) / (6 + 3) = 18 / 9 = 2 Ω.
Step 2, total resistance: R = 2 + 4 = 6 Ω.
Step 3, total current: I = V / R = 12 / 6 = 2 A.
Step 4, voltage across the parallel part: V = I × Rp = 2 × 2 = 4 V.
Step 5, branch currents: I6Ω = 4 / 6 ≈ 0.67 A and I3Ω = 4 / 3 ≈ 1.33 A. Check: 0.67 + 1.33 = 2 A, which matches the total.
Common mistake: adding parallel resistors as if they were in series. The combined parallel value is always smaller than the smallest resistor.
Problem 4: Force on a current-carrying conductor
A straight wire 0.5 m long carries a current of 4 A at right angles to a magnetic field of 0.2 T. Find the force on the wire.
Formula: F = B I l sin θ, and sin 90° = 1
Solution: F = 0.2 × 4 × 0.5 × 1 = 0.4 N.
Common mistake: forgetting the sin θ term when the wire is not at 90° to the field.
Problem 5: Electromagnetic induction
A coil of 200 turns has its magnetic flux reduced from 0.05 Wb to 0.01 Wb in 0.2 s. Find the magnitude of the induced emf.
Formula: |ε| = N × (change in flux) / (time)
Solution: Change in flux = 0.05 − 0.01 = 0.04 Wb. |ε| = 200 × 0.04 / 0.2 = 200 × 0.2 = 40 V.
Note: By Lenz's law, the direction of the induced current opposes the decrease in flux. If the question asks for direction, say so in words.
Common mistake: leaving out N, the number of turns.
Problem 6: Convex lens
An object is placed 30 cm in front of a convex lens of focal length 10 cm. Find the image distance and the magnification.
Sign convention (new Cartesian): distances are measured from the lens. u is negative for an object on the left, and f is positive for a convex lens. Use the convention in your textbook.
Given: u = −30 cm, f = +10 cm
Formula: 1/v − 1/u = 1/f
Solution: 1/v = 1/f + 1/u = 1/10 − 1/30 = 3/30 − 1/30 = 2/30, so v = +15 cm. Magnification m = v/u = 15 / (−30) = −0.5.
Meaning: v is positive, so the image is real and on the other side of the lens. m is negative and has magnitude less than 1, so the image is inverted and smaller than the object.
Common mistake: dropping the minus sign on u.
Problem 7: Photoelectric effect
Light of wavelength 400 nm falls on a metal whose work function is 2.0 eV. Find the maximum kinetic energy of the emitted electrons.
Useful value: hc ≈ 1240 eV nm
Formula: Kmax = hν − φ = (hc / λ) − φ
Solution: Photon energy = 1240 / 400 = 3.1 eV. Kmax = 3.1 − 2.0 = 1.1 eV, which is about 1.76 × 10−19 J. The stopping potential is therefore 1.1 V.
Common mistake: mixing eV and joule. Convert only at the end, using 1 eV = 1.6 × 10−19 J. If your textbook gives different constants, use those.
Problem 8: Radioactive decay
A radioactive sample of 80 g has a half-life of 4 days. How much remains after 12 days?
Solution: Number of half-lives = 12 / 4 = 3. Remaining = 80 × (½)3 = 80 / 8 = 10 g.
Common mistake: dividing by 2 only once, or using the days directly as the power.
Five habits that save marks
- Always write the unit with every value and in the final answer.
- Convert prefixes (μ, m, k) before you substitute.
- Keep your signs: negative u, negative charge, direction of induced current.
- Do a quick sense check. A force of 1020 N between two small charges means a power-of-ten error.
- Show every step. Even if the final answer is wrong, correct steps and formulas earn marks.
Frequently asked questions
How many numericals should I practise each day?
Start with 5 to 8 problems and review each mistake. The quality of your review matters more than the number.
Should I memorise values like k or hc?
Use the values given in your textbook or question paper. Memorise the formulas and the common constants your teacher recommends.
Do these problems come in the exam?
These are practice problems written by us, not exam questions. They show the style of working, which applies to any numerical.
Key takeaways
- Use the 5-step method: given, units, formula, substitute, answer with unit.
- Most lost marks come from units, powers of ten and signs.
- Practise with your own mistake list and revise it before every exam.
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