Answer :

Given: Temperature coefficient of filament,

α = 1.70 × 10^{-4} per °C

Let T_{1} be the temperature of element, R_{1} = 100Ω (Given: T_{1} = 27°C)

Let T_{2} be the temperature of element, R_{2} = 117Ω

To find T_{2} = ?

The formula is: R_{2} = R_{1}[1 + α(T_{2}-T_{1})]

⇒ R_{2} - R_{1} = R_{1}α(T_{2} - T_{1})

⇒ R_{2} - R_{1} = R_{1}α (T_{2} - T_{1})

⇒

⇒ T_{2}-27°C = 1000°C

⇒ T_{2} = 1000°C + 27°C

Hence Temperature of element, T_{2} is 1027 °C.

__Note: The temperature coefficient of resistance (α) gives the change in resistance per degree change in temperature. For pure metals, it is positive means- The resistance increases with temperature.__

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