If a Wire Resistance is 10 ohm at 0 DegC and the same wire Resistance becomes 15 ohm at temperature 100 DegC, then at what temperature the wire Resistance will be 30 ohm? Temperature coefficient of the wire material is 0.0047.

resistance=Ro(1+.0047T)

Ro=10 ohm, given
check:
R@100=10(1+.0047*100)=10(1+.45)=15ohm

30=10(1+.0047T)
3=1+.0047T
T=2/.0047=426C

To find the temperature at which the wire resistance will be 30 ohms, we need to use the formula for temperature dependence of resistance, which is given by:

Rt = Ro * (1 + α * ΔT)

Where:
Rt = Resistance at temperature t
Ro = Resistance at reference temperature (0°C in this case)
α = Temperature coefficient of the wire material
ΔT = Change in temperature from reference temperature to t

First, let's calculate the change in resistance for the given change in temperature:

ΔR = Rt - Ro

Knowing that at 0°C, the resistance is 10 ohms, and at 100°C, the resistance is 15 ohms, we can calculate ΔR:

ΔR = 15 ohms - 10 ohms = 5 ohms

Next, we need to calculate the change in temperature (ΔT) that corresponds to the change in resistance (ΔR). Rearranging the formula, we have:

ΔT = ΔR / (Ro * α)

Plugging in the values:

ΔT = 5 ohms / (10 ohms * 0.0047) = 106.38°C

So, the change in temperature is 106.38°C for a resistance change of 5 ohms.

Now, we can find the temperature (t) at which the resistance will be 30 ohms by rearranging the formula:

Rt = Ro * (1 + α * ΔT)

t = ΔT + reference temperature

Substituting the known values:

t = 106.38°C + 0°C = 106.38°C

Therefore, the wire resistance will be 30 ohms at a temperature of 106.38°C.