Question

Resistance of a 3m wire in Dhaka (at 30 degree centigrade) is 25 Ohm. What will be the resistance of the same wire at Moscow? (The temperature of Moscow now-a-days is near to 67 degree Fahrenheit.)​

Answer 1

Given info : Resistance of a 3m wire in Dhaka (at 30 degree centigrade) is 25 Ohm.

To find : the resistance of the same wire at Moscow where Temperature is near to 67° Fahrenheit. )

Solution : first convert °F into °C

Using formula, (C -0)/5 = (F - 32)/9

⇒C = 5(67 - 32)/9 = 5 × 35/9 = 175/9 = 19.44°C

case 1 : resistance of the wire is 25 ohm at 30°

Using formula, R = R₀[1 + α∆T]......(a)

Let resistance at 0°C is R₀

So, 25 ohm = R₀[1 + α × 30°C].......(1)

Case 2 : let R is the resistance of wire at 19.44°C (or 67°F)

From formula (a), R = R₀ [1 + α × 19.44°C]......(2)

From equations (1) and (2) we get,

25/R = (1 + 30α)/(1 + 19.44α)

⇒25 + 25 × 19.44α = (1 +30α)R

⇒(25 + 486α)/(1 + 30α) = R

So the resistance of the same wire would be (25 + 486α)/(1 + 30α) where α is coefficient of resistance.