Question

Calculate the resistance of a nichrome wire, which will bring 200 g of water at 20°C to its boiling point in 7 minutes, when the current flowing through the wire is 4 A.

Answer 1

I = 4 A; t = 7 min = 420 s; R = ?

m = 200 g; SHC of water = 4.2 Jg⁻¹°C⁻¹;  θ_R = (100 − 20)°C = 80°C

Energy produced in wire = I² × R × t

= 4² × R × 420 J

= 16 × R × 420 J

Energy absorbed by water = m c θ_R

= 200 × 4.2 × 80 J

∴ By the law of conservation of energy

16 × R × 420 = 200 × 4.2 × 80

\[\text{R} = \frac{200 \times 4.2 \times 80}{16 \times 420}\]

\[= \frac{67200}{6720}\]

= 10 Ω