how much would you have to raise the temperature of a copper wire(originally at 20degree celcius) to increase its resistance by 15%? express your answer in percentage.note a=0.0068per degree celcius
To find the increase in temperature required to increase the resistance of a copper wire by 15%, we can use the following formula:
ΔR = R0 * α * ΔT
Where:
ΔR = Change in resistance
R0 = Initial resistance
α = Temperature coefficient of copper (given as 0.0068 per degree Celsius)
ΔT = Change in temperature
Since we are given the percentage increase in resistance and want to find the percentage increase in temperature, we can rearrange the formula as follows:
(ΔT / T0) = (ΔR / R0) / α
Given that the initial temperature is 20 degrees Celsius and the desired increase in resistance is 15%, we can substitute the values into the formula:
(ΔT / 20) = (0.15 / 1) / 0.0068
Simplifying the expression:
ΔT = (0.15 / 1) / 0.0068 * 20
ΔT = 2.205882353 * 20
ΔT ≈ 44.1182353 degrees Celsius
Therefore, you would need to raise the temperature of the copper wire by approximately 44.12 degrees Celsius in order to increase its resistance by 15%.
To find the increase in temperature needed to increase the resistance of a copper wire by 15%, you need to use the formula:
R2 = R1 * (1 + a * ΔT)
Where:
R1 is the initial resistance of the wire,
R2 is the resistance after the increase,
a is the temperature coefficient of resistance for copper (0.0068 per degree Celsius),
ΔT is the change in temperature.
Let's solve for ΔT. We know that R2 = R1 * 1.15 (increase resistance by 15%).
R1 * 1.15 = R1 * (1 + a * ΔT)
Dividing both sides by R1:
1.15 = 1 + a * ΔT
Subtracting 1 from both sides:
0.15 = a * ΔT
Finally, solving for ΔT:
ΔT = 0.15 / a
Substituting the given value for a (0.0068 per degree Celsius):
ΔT = 0.15 / 0.0068
ΔT ≈ 22.0588 degrees Celsius
Therefore, you would need to raise the temperature of the copper wire by approximately 22.06 degrees Celsius to increase its resistance by 15%.
Ro + Ro*0.0068/oC*(T2 -T1) = 1.15Ro.
Divide both sides by Ro:
0.0068/oC*(T2-20) = 1.15,
T2-20 = 169,
T2 = 189oC.
%Increase = ((T2-T1)/T1)*100%
%Increase = ((189-20)/20)100 = 845%.