Resistivity and resistance of a wire: Class 10 practice
R = ρL/A. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Area of a circle
- Scientific notation
The idea behind resistivity and resistance of a wire
R = ρL/A. Resistance increases with length and decreases with cross-sectional area. Stretching a wire to n times its length (same volume) makes its resistance n² times.
Step-by-step method
- Write ρ, L and A in SI units.
- Use R = ρL/A.
- For stretching, keep volume constant: A falls as L rises.
Worked example 1 (Basic)
Find the resistance of a 3 m wire of area 2 mm² and resistivity 1.1e-6 Ω m.
- A = 2 × 10⁻⁶ m²
- R = ρL/A = 1.650e+0 Ω
- Answer: 1.650e+0 Ω
Worked example 2 (Standard)
A wire of length 17 m and area 1.5 mm² has resistance 1.927e-1 Ω. Find its resistivity.
- ρ = RA/L
- = 1.70e-8 Ω m
- Answer: 1.70e-8 Ω m
Worked example 3 (Challenge)
A 15 Ω wire is stretched to 4 times its length (volume unchanged). Find its new resistance.
- L → 4L, A → A/4
- R → 16R = 240 Ω
- Answer: 240 Ω
Common mistakes and misconceptions
- Using diameter instead of radius for A
- Thinking stretching only doubles R
Practice questions
- (Basic) Find the resistance of a 9 m wire of area 2 mm² and resistivity 1.1e-6 Ω m.
- (Basic) Find the resistance of a 5 m wire of area 2 mm² and resistivity 1.7e-8 Ω m.
- (Standard) A wire of length 8 m and area 1.5 mm² has resistance 1.493e-1 Ω. Find its resistivity.
- (Standard) A wire of length 2 m and area 0.5 mm² has resistance 1.120e-1 Ω. Find its resistivity.
- (Challenge) A 11 Ω wire is stretched to 4 times its length (volume unchanged). Find its new resistance.
- (Challenge) A 13 Ω wire is stretched to 2 times its length (volume unchanged). Find its new resistance.
Answer key with full working
- Q1: A = 2 × 10⁻⁶ m² → R = ρL/A = 4.950e+0 Ω → Answer: 4.950e+0 Ω
- Q2: A = 2 × 10⁻⁶ m² → R = ρL/A = 4.250e-2 Ω → Answer: 4.250e-2 Ω
- Q3: ρ = RA/L → = 2.80e-8 Ω m → Answer: 2.80e-8 Ω m
- Q4: ρ = RA/L → = 2.80e-8 Ω m → Answer: 2.80e-8 Ω m
- Q5: L → 4L, A → A/4 → R → 16R = 176 Ω → Answer: 176 Ω
- Q6: L → 2L, A → A/2 → R → 4R = 52 Ω → Answer: 52 Ω
Syllabus note
This skill is listed under "Electricity" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
- Electricity chapter notes (Class 10)
- Ohm's law and resistors in series and parallel
- Electric power and energy consumption
- Heating effect of current (Joule's law)
- Mixed series–parallel circuits
- Power rating, current and fuse choice
- Charge, current and number of electrons
- Lens formula and magnification
- Mirror formula and magnification
- Refractive index and speed of light
- Power of a lens and lens combinations
- All Class 10 practice
Frequently asked questions
Which chapter is resistivity and resistance of a wire in?
"Electricity", Class 10 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.