JEE Main 2021 — Current Electricity Question with Solution

Given, the length of the water pipe, L = 1 m

The cross-sectional area of the water pipe, A = 1 cm² = 10^$$-$$4 m²

The temperature of the ice = $$-$$ 10$${}^{\circ }$$C

Current passing in the conductor, I = 0.5 A

Resistance of the conductor, R = 4 k$$\Omega$$

The latent heat of fusion for ice, L_f = 3.33 $$\times$$ 10⁵ J/kg

The density of the ice, d = 1000 kg/m³

The specific heat of the ice, c_{p, ice} = 2 $$\times$$ 10³ J/kg

Heat required to melt the ice at 10$${}^{\circ }$$C to 0$${}^{\circ }$$C

Q = mc_p$$\Delta$$T + mL_f $$\Rightarrow$$ Q = dVc_p$$\Delta$$T + dVL_f

= 1000 $$\times$$ 10^$$-$$4 $$\times$$ 2 $$\times$$ 10³ $$\times$$ (10) + 1000 $$\times$$ 10^$$-$$4 $$\times$$ 3.33 $$\times$$ 10⁵ ($$\because$$ V = A $$\times$$ L)

= 35300 J

According to the Joule's law of heating,

H = I²Rt

$$\Rightarrow$$ 35300 = (0.5)²(4000) (t)

$$\Rightarrow$$ t = 35.3 s

Thus, the minimum time required to melt the ice is 35.3 s.